This document discusses methods for improving perceptron decision trees (PDTs) by enlarging their margins. It proposes three algorithms:
1. FAT (Find-And-Replace Trees) post-processes existing decision trees by replacing each node's decision with an optimal separating hyperplane found via perceptron learning, maximizing the margin.
2. MOC1 (Margin OC1) modifies the OC1 algorithm to use a multi-objective splitting criterion that maximizes both information gain and margin size.
3. MOC2 modifies the splitting criterion (Twoing rule) to incorporate margin. Experimental results show FAT and MOC1 generalize better than the basic OC1 algorithm on benchmark datasets.
The document defines key concepts related to limits and derivatives:
1) It defines left-hand and right-hand limits and discusses how the limit of a function is defined if the left and right limits coincide.
2) It provides examples of evaluating limits of functions, including limits involving polynomials, rational functions, and trigonometric functions.
3) It discusses properties of limits, such as the algebra of limits and the sandwich theorem.
4) It introduces the definition of the derivative as the limit of the difference quotient, and defines the derivative of a function at a point. It also discusses the algebra of derivatives and lists some standard derivative rules.
This document discusses key concepts in probability theory, including:
1) Markov's inequality and Chebyshev's inequality, which relate the probability that a random variable exceeds a value to its expected value and variance.
2) The weak law of large numbers and central limit theorem, which describe how the means of independent random variables converge to the expected value and follow a normal distribution as the number of variables increases.
3) Stochastic processes, which are collections of random variables indexed by time or another parameter and can model evolving systems. Examples of stochastic processes and their properties are provided.
1. The document discusses maximum likelihood estimation and Bayesian parameter estimation for machine learning problems involving parametric densities like the Gaussian.
2. Maximum likelihood estimation finds the parameter values that maximize the probability of obtaining the observed training data. For Gaussian distributions with unknown mean and variance, MLE returns the sample mean and variance.
3. Bayesian parameter estimation treats the parameters as random variables and uses prior distributions and observed data to obtain posterior distributions over the parameters. This allows incorporation of prior knowledge with the training data.
The document discusses probability distributions and their natural parameters. It provides examples of several common distributions including the Bernoulli, multinomial, Gaussian, and gamma distributions. For each distribution, it derives the natural parameter representation and shows how to write the distribution in the form p(x|η) = h(x)g(η)exp{η^T μ(x)}. Maximum likelihood estimation for these distributions is also briefly discussed.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document presents a theorem that establishes the existence of a fixed point for a mapping under a general contractive condition of integral type. The mapping considered generalizes various types of contractive mappings in an integral setting. The theorem proves that if a self-mapping on a complete metric space satisfies the given integral inequality involving the distance between images of points, where the integral involves a non-negative, summable function, then the mapping has a unique fixed point. Furthermore, the sequence of repeated applications of the mapping to any starting point will converge to this fixed point. The proof involves showing the distance between successive terms in the sequence decreases according to the integral inequality.
The document reviews concepts related to random variables and random processes. It defines key terms such as:
- Discrete and continuous random variables and their probability distribution and density functions.
- Joint, marginal, and conditional density functions which describe the relationships between multiple random variables.
- Independent and orthogonal random variables, and concepts like inner products, that are used to analyze relationships between random variables.
- Various types of convergence for sequences of random variables such as almost sure, mean square, and in probability which are important for analyzing random processes over time.
The review covers critical foundational concepts for understanding and working with random variables and stochastic processes.
This document provides an overview of probability theory concepts related to random variables. It defines random variables and their probability mass functions and cumulative distribution functions. It describes different types of random variables including discrete, continuous, Bernoulli, binomial, geometric, Poisson, uniform, exponential, gamma, and normal random variables. It also covers concepts of joint and marginal distributions as well as independent and conditional random variables. The document uses mathematical notation to formally define these concepts.
This document defines and provides examples of expectation, or the average value, of random variables. It discusses properties of expectations including how the expectation of a function of a random variable is calculated. It also defines and gives properties of variance, covariance, conditional expectation, and conditional variance. Examples are provided throughout to illustrate key concepts.
The document defines key concepts related to limits and derivatives:
1) It defines left-hand and right-hand limits and discusses how the limit of a function is defined if the left and right limits coincide.
2) It provides examples of evaluating limits of functions, including limits involving polynomials, rational functions, and trigonometric functions.
3) It discusses properties of limits, such as the algebra of limits and the sandwich theorem.
4) It introduces the definition of the derivative as the limit of the difference quotient, and defines the derivative of a function at a point. It also discusses the algebra of derivatives and lists some standard derivative rules.
This document discusses key concepts in probability theory, including:
1) Markov's inequality and Chebyshev's inequality, which relate the probability that a random variable exceeds a value to its expected value and variance.
2) The weak law of large numbers and central limit theorem, which describe how the means of independent random variables converge to the expected value and follow a normal distribution as the number of variables increases.
3) Stochastic processes, which are collections of random variables indexed by time or another parameter and can model evolving systems. Examples of stochastic processes and their properties are provided.
1. The document discusses maximum likelihood estimation and Bayesian parameter estimation for machine learning problems involving parametric densities like the Gaussian.
2. Maximum likelihood estimation finds the parameter values that maximize the probability of obtaining the observed training data. For Gaussian distributions with unknown mean and variance, MLE returns the sample mean and variance.
3. Bayesian parameter estimation treats the parameters as random variables and uses prior distributions and observed data to obtain posterior distributions over the parameters. This allows incorporation of prior knowledge with the training data.
The document discusses probability distributions and their natural parameters. It provides examples of several common distributions including the Bernoulli, multinomial, Gaussian, and gamma distributions. For each distribution, it derives the natural parameter representation and shows how to write the distribution in the form p(x|η) = h(x)g(η)exp{η^T μ(x)}. Maximum likelihood estimation for these distributions is also briefly discussed.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document presents a theorem that establishes the existence of a fixed point for a mapping under a general contractive condition of integral type. The mapping considered generalizes various types of contractive mappings in an integral setting. The theorem proves that if a self-mapping on a complete metric space satisfies the given integral inequality involving the distance between images of points, where the integral involves a non-negative, summable function, then the mapping has a unique fixed point. Furthermore, the sequence of repeated applications of the mapping to any starting point will converge to this fixed point. The proof involves showing the distance between successive terms in the sequence decreases according to the integral inequality.
The document reviews concepts related to random variables and random processes. It defines key terms such as:
- Discrete and continuous random variables and their probability distribution and density functions.
- Joint, marginal, and conditional density functions which describe the relationships between multiple random variables.
- Independent and orthogonal random variables, and concepts like inner products, that are used to analyze relationships between random variables.
- Various types of convergence for sequences of random variables such as almost sure, mean square, and in probability which are important for analyzing random processes over time.
The review covers critical foundational concepts for understanding and working with random variables and stochastic processes.
This document provides an overview of probability theory concepts related to random variables. It defines random variables and their probability mass functions and cumulative distribution functions. It describes different types of random variables including discrete, continuous, Bernoulli, binomial, geometric, Poisson, uniform, exponential, gamma, and normal random variables. It also covers concepts of joint and marginal distributions as well as independent and conditional random variables. The document uses mathematical notation to formally define these concepts.
This document defines and provides examples of expectation, or the average value, of random variables. It discusses properties of expectations including how the expectation of a function of a random variable is calculated. It also defines and gives properties of variance, covariance, conditional expectation, and conditional variance. Examples are provided throughout to illustrate key concepts.
This document provides an overview of Markov chain Monte Carlo (MCMC) methods. It begins with motivations for using MCMC, such as dealing with latent variable models where the likelihood function is intractable. It then covers random variable generation techniques before introducing the key MCMC algorithms: the Metropolis-Hastings algorithm and the Gibbs sampler. The document outlines the remaining topics to be covered, which include Monte Carlo integration, notions of Markov chains, and further advanced topics.
This document discusses likelihood methods for continuous-time models in finance. It describes approximating the transition density function pX of a continuous-time process through a series of transformations to get closer to a normal distribution. This allows representing pX as a series expansion involving Hermite polynomials. Computing the expansion coefficients allows obtaining an explicit closed-form approximation to pX. Maximizing the approximate likelihood results in an estimator that converges to the true MLE as the number of terms increases.
CVPR2010: higher order models in computer vision: Part 1, 2zukun
This document discusses tractable higher order models in computer vision using random field models. It introduces Markov random fields (MRFs) and factor graphs as graphical models for computer vision problems. Higher order models that include factors over cliques of more than two variables can model problems more accurately but are generally intractable. The document discusses various inference techniques for higher order models such as relaxation, message passing, and decomposition methods. It provides examples of how higher order and global models can be used in problems like segmentation, stereo matching, reconstruction, and denoising.
This document provides an overview of Bayesian methods for machine learning. It introduces some foundational Bayesian concepts including representing beliefs with probabilities, the Dutch book theorem, asymptotic certainty, and model comparison using Occam's razor. It discusses challenges like intractable integrals and presents approximation tools like Laplace's approximation, variational inference, and MCMC. It also covers choosing priors, including objective priors like noninformative, Jeffreys, and reference priors as well as subjective and hierarchical priors.
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
The document derives the normal probability density function from basic assumptions. It assumes that errors in perpendicular directions are independent, large errors are less likely than small errors, and the distribution is not dependent on orientation. This leads to a differential equation that can only be satisfied by an exponential function, giving the normal distribution. The values of the coefficients are determined by requiring the total area under the curve to be 1 and that the variance equals 1/k. This fully specifies the normal probability density function.
Senior Seminar: Systems of Differential EquationsJDagenais
This document discusses solving systems of differential equations. It begins by introducing systems of differential equations and their importance in modeling natural processes. It then outlines the key concepts needed to solve systems, including matrices, eigenvalues, and diagonalization. The document focuses on solving homogeneous systems where the eigenvalues are distinct and real. It presents the process of writing systems in matrix form and looking for solutions of the form x=e^rt to find the eigenvalues from the characteristic equation.
This document provides an introduction to predicate logic. It discusses how predicate logic builds on propositional logic using quantifiers, predicates, and logical connectives. It presents the basic approach of stripping and reinserting quantifiers when proving arguments. It then introduces four new inference rules for quantifier stripping and insertion. Several examples are provided demonstrating how to construct proofs of arguments using these rules. The document also discusses using temporary hypotheses and proving verbal arguments in predicate logic.
EM algorithm and its application in probabilistic latent semantic analysiszukun
The document discusses the EM algorithm and its application in Probabilistic Latent Semantic Analysis (pLSA). It begins by introducing the parameter estimation problem and comparing frequentist and Bayesian approaches. It then describes the EM algorithm, which iteratively computes lower bounds to the log-likelihood function. Finally, it applies the EM algorithm to pLSA by modeling documents and words as arising from a mixture of latent topics.
The document discusses calculating volumes of solids of revolution. It provides examples of finding the volume when revolving common shapes around different axes, such as:
(1) Revolving a cone around the x-axis to find the volume is 1/3πr2h.
(2) Revolving a sphere around the x or y-axis finds the volume is 4/3πr3.
(3) Revolving the region between y=x2 and the y-axis around the y-axis from 0 to 1 finds the volume is π/2 units3.
The presentation gives basic insight into Information Theory, Entropies, various binary channels, and error conditions. It explains principles, derivations and problems in very easy and detailed manner with examples.
This document summarizes a lecture on modern physics and quantum mechanics. It discusses infinite potential barriers, finite potential barriers, and quantum tunneling. For an infinite barrier, particles reflect completely. For a finite barrier, particles can partially penetrate the barrier due to quantum tunneling, with probability of penetration decreasing as the barrier height or width increases.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Matthew Leingang
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Daniel Romo is moving his research group from Texas A&M University to Baylor University in August 2015. His group conducts synthetic, biological, and biosynthetic studies of bioactive natural products with a focus on developing novel synthetic strategies and understanding the mode of action of natural products through activity-based proteomic profiling and molecular studies. Current projects include the total synthesis of oxazolomycin and gracillins and investigating the mechanisms of rameswaralide, ophiobolin, and agelastatin A.
Estrategia y planificación - No presentado - Taller Internet PyME EARTHPaul Fervoy
Esta presentación habla acerca del proceso de planificación de la presencia web. No se vio durante el Taller.
Por Paul Fervoy para Universidad EARTH en al Cuarto Taller para Pequeños Productores y Organizaciones. Noviembre 28, 29 y 30 en EARTH Guápiles Costa Rica. Para más información sobre el Taller, contácte Jan Axelsson (jaxelsson@earth.ac.cr).
E-Learning y correo electrónico- herramienta gratuita.Johanna Saenz
Las herramientas de comunicación como el chat, videoconferencia, correo electrónico y foros de discusión son elementos indispensables para los cursos en línea, ya que permiten la interacción entre estudiantes y profesores de manera síncrona o asíncrona. El correo electrónico es un servicio que permite el intercambio rápido de mensajes y archivos entre dispositivos a través del protocolo SMTP, y se actualiza con los mensajes recibidos y enviados que quedan almacenados en bandejas separadas.
- Durmazlar has been producing press brakes since 1956 at its contemporary production plants with 1000 employees and 150,000 sqm footprint.
- It developed a Research & Development Center in 2010 to design press brakes equipped with quality components to precisely meet customer needs.
- Durmazlar aims to serve customers with high performance, accuracy, speed, flexibility, durability, reliability and advanced technology at a high performance to price ratio supported by a global distributor and service network.
This document provides an overview of Markov chain Monte Carlo (MCMC) methods. It begins with motivations for using MCMC, such as dealing with latent variable models where the likelihood function is intractable. It then covers random variable generation techniques before introducing the key MCMC algorithms: the Metropolis-Hastings algorithm and the Gibbs sampler. The document outlines the remaining topics to be covered, which include Monte Carlo integration, notions of Markov chains, and further advanced topics.
This document discusses likelihood methods for continuous-time models in finance. It describes approximating the transition density function pX of a continuous-time process through a series of transformations to get closer to a normal distribution. This allows representing pX as a series expansion involving Hermite polynomials. Computing the expansion coefficients allows obtaining an explicit closed-form approximation to pX. Maximizing the approximate likelihood results in an estimator that converges to the true MLE as the number of terms increases.
CVPR2010: higher order models in computer vision: Part 1, 2zukun
This document discusses tractable higher order models in computer vision using random field models. It introduces Markov random fields (MRFs) and factor graphs as graphical models for computer vision problems. Higher order models that include factors over cliques of more than two variables can model problems more accurately but are generally intractable. The document discusses various inference techniques for higher order models such as relaxation, message passing, and decomposition methods. It provides examples of how higher order and global models can be used in problems like segmentation, stereo matching, reconstruction, and denoising.
This document provides an overview of Bayesian methods for machine learning. It introduces some foundational Bayesian concepts including representing beliefs with probabilities, the Dutch book theorem, asymptotic certainty, and model comparison using Occam's razor. It discusses challenges like intractable integrals and presents approximation tools like Laplace's approximation, variational inference, and MCMC. It also covers choosing priors, including objective priors like noninformative, Jeffreys, and reference priors as well as subjective and hierarchical priors.
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
The document derives the normal probability density function from basic assumptions. It assumes that errors in perpendicular directions are independent, large errors are less likely than small errors, and the distribution is not dependent on orientation. This leads to a differential equation that can only be satisfied by an exponential function, giving the normal distribution. The values of the coefficients are determined by requiring the total area under the curve to be 1 and that the variance equals 1/k. This fully specifies the normal probability density function.
Senior Seminar: Systems of Differential EquationsJDagenais
This document discusses solving systems of differential equations. It begins by introducing systems of differential equations and their importance in modeling natural processes. It then outlines the key concepts needed to solve systems, including matrices, eigenvalues, and diagonalization. The document focuses on solving homogeneous systems where the eigenvalues are distinct and real. It presents the process of writing systems in matrix form and looking for solutions of the form x=e^rt to find the eigenvalues from the characteristic equation.
This document provides an introduction to predicate logic. It discusses how predicate logic builds on propositional logic using quantifiers, predicates, and logical connectives. It presents the basic approach of stripping and reinserting quantifiers when proving arguments. It then introduces four new inference rules for quantifier stripping and insertion. Several examples are provided demonstrating how to construct proofs of arguments using these rules. The document also discusses using temporary hypotheses and proving verbal arguments in predicate logic.
EM algorithm and its application in probabilistic latent semantic analysiszukun
The document discusses the EM algorithm and its application in Probabilistic Latent Semantic Analysis (pLSA). It begins by introducing the parameter estimation problem and comparing frequentist and Bayesian approaches. It then describes the EM algorithm, which iteratively computes lower bounds to the log-likelihood function. Finally, it applies the EM algorithm to pLSA by modeling documents and words as arising from a mixture of latent topics.
The document discusses calculating volumes of solids of revolution. It provides examples of finding the volume when revolving common shapes around different axes, such as:
(1) Revolving a cone around the x-axis to find the volume is 1/3πr2h.
(2) Revolving a sphere around the x or y-axis finds the volume is 4/3πr3.
(3) Revolving the region between y=x2 and the y-axis around the y-axis from 0 to 1 finds the volume is π/2 units3.
The presentation gives basic insight into Information Theory, Entropies, various binary channels, and error conditions. It explains principles, derivations and problems in very easy and detailed manner with examples.
This document summarizes a lecture on modern physics and quantum mechanics. It discusses infinite potential barriers, finite potential barriers, and quantum tunneling. For an infinite barrier, particles reflect completely. For a finite barrier, particles can partially penetrate the barrier due to quantum tunneling, with probability of penetration decreasing as the barrier height or width increases.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Matthew Leingang
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Daniel Romo is moving his research group from Texas A&M University to Baylor University in August 2015. His group conducts synthetic, biological, and biosynthetic studies of bioactive natural products with a focus on developing novel synthetic strategies and understanding the mode of action of natural products through activity-based proteomic profiling and molecular studies. Current projects include the total synthesis of oxazolomycin and gracillins and investigating the mechanisms of rameswaralide, ophiobolin, and agelastatin A.
Estrategia y planificación - No presentado - Taller Internet PyME EARTHPaul Fervoy
Esta presentación habla acerca del proceso de planificación de la presencia web. No se vio durante el Taller.
Por Paul Fervoy para Universidad EARTH en al Cuarto Taller para Pequeños Productores y Organizaciones. Noviembre 28, 29 y 30 en EARTH Guápiles Costa Rica. Para más información sobre el Taller, contácte Jan Axelsson (jaxelsson@earth.ac.cr).
E-Learning y correo electrónico- herramienta gratuita.Johanna Saenz
Las herramientas de comunicación como el chat, videoconferencia, correo electrónico y foros de discusión son elementos indispensables para los cursos en línea, ya que permiten la interacción entre estudiantes y profesores de manera síncrona o asíncrona. El correo electrónico es un servicio que permite el intercambio rápido de mensajes y archivos entre dispositivos a través del protocolo SMTP, y se actualiza con los mensajes recibidos y enviados que quedan almacenados en bandejas separadas.
- Durmazlar has been producing press brakes since 1956 at its contemporary production plants with 1000 employees and 150,000 sqm footprint.
- It developed a Research & Development Center in 2010 to design press brakes equipped with quality components to precisely meet customer needs.
- Durmazlar aims to serve customers with high performance, accuracy, speed, flexibility, durability, reliability and advanced technology at a high performance to price ratio supported by a global distributor and service network.
En este curso de 12 horas aprenderá la importancia que hoy tiene la generación de comunidad y la administración mediante el conocido sistema de gerencia de relaciones con el cliente (CRM), con la importante implicación que representa la comunicación social por medio de los usuarios del ecosistema digital de la empresa. Además, conocerá las principales herramientas y aplicaciones para ejercer la actividad de seguimiento de sus clientes.
El docente del curso es Pablo Di Meglio, reconocido especialista y conferencista en temas relacionados al Marketing Digital y Social Media, y con más de 6 años de experiencia implementando estrategias en redes sociales para empresas como DIRECTV, SAP, CABLEVISION, SAP MILLER y Nextel entre otras.
Cómo diseñar innovaciones desde el análisis de las tendencias de consumo.
Comment concevoir des innovations à partir de l'analyse des tendances de consommation.
How to design innovations from the analysis of consumer trends.
SAMSUNG Wireless LAN solution grows with new tools and devices (new AP controller and new APs 802.11ac).
Look at the new brochure coming from official SAMSUNG Business site: https://www.samsungbusiness.com/business/pages/main/downloads/brochures.aspx
This document provides information on Rockfon Fibral Alu and Fibral Alu Shadowline ceiling panels. It describes the product as 100% inorganic stone wool panels with an aluminum painted front surface and sound absorbing properties. Details are given on panel sizes, edges, light reflection, weight, fire resistance, sound absorption, humidity resistance, demountability, recycling, and how Rockfon ceilings can actively improve buildings.
Comercio Justo. Oportunidades de Negocios.enendeavor
El documento habla sobre las oportunidades de negocio en el segmento de comercio justo. Explica que el comercio justo busca mayor equidad en el comercio internacional al ofrecer mejores condiciones a productores y trabajadores en desventaja. También describe varias organizaciones de comercio justo en Argentina y los productos más comúnmente certificados a nivel global con el sello de comercio justo.
This document describes a study using molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) methods to analyze the binding energetics and identify interaction hot spots in complexes between a camel single chain antibody (cAb-Lys3) and two lysozyme antigens (hen egg white lysozyme and turkey egg white lysozyme). The study involves molecular dynamics simulations of the complexes followed by MM/PBSA free energy decomposition to determine the contribution of individual amino acids to complex formation. Key hot spot residues in the antibody that make important contributions to binding are identified. The study provides insights that could inform rational design of small molecule mimics of the antibody.
Conexión de Samsung F480 a un PC mediante Bluetoothladynoa
Este documento explica cómo conectar un teléfono Samsung modelo F480 a un ordenador mediante un adaptador Bluetooth USB. Detalla los pasos para instalar el adaptador USB en el ordenador con Windows 7, configurar el Bluetooth en el teléfono Samsung para hacerlo visible, y realizar la conexión escaneando los dispositivos Bluetooth disponibles y emparejándolos mediante la introducción de un PIN compartido. Una vez conectados, permite enviar y recibir archivos entre el teléfono y el ordenador a través de Bluetooth.
Este documento presenta las reglas básicas para jugar el juego de cartas de combate Card Wars. El objetivo del juego es reducir los puntos de vida del oponente de 25 a 0. Cada jugador controla una baraja de 40 cartas que incluyen criaturas, edificios y hechizos para combatir en cuatro carriles. Durante su turno, un jugador puede jugar cartas, activar habilidades como "Floop", y atacar con sus criaturas listas. Las criaturas en combate se dañan mutuamente dependiendo de sus
The document provides an introduction to mobile networks and mobile broadband, covering the evolution from GSM to LTE. It discusses key aspects of GSM, GPRS, UMTS, HSPA and LTE including network elements, air interfaces, mobility management, and data services. The document is intended to explain the core concepts and technologies underlying modern cellular networks.
Este manual proporciona instrucciones sobre cómo jugar al videojuego SWAT 4, incluyendo los requisitos del sistema, cómo instalar el juego, navegar por los menús y opciones, jugar partidas individuales y multijugador, y una guía sobre cómo jugar efectivamente completando misiones como líder de un equipo SWAT.
Acxiom’s Retail Consumer Dynamics Study provides a consumer-centric snapshot of the UK retail market based on current consumer thinking and behaviour underpinned by a wealth of demography and lifestyle intelligence.
Read on to find out more.
Presentació de El Portal de la Recerca de Catalunya a les 4es Jornades sobre Gestió de la Informació Científica (JGIC 2015) dels dies 21 i 22 de maig del 2015, a cárrec d'Enric Canela (UB) i Lluís Anglada (CSUC) amb el suport de Sandra Reoyo (CSUC), Ricard de la Vega (CSUC) i Ramon Ros (CSUC).
Este documento describe los pasos para montar una arquitectura cliente-servidor bajo Windows utilizando virtualización. Se implementarán 3 servidores virtuales: un controlador de dominio principal, un controlador de dominio secundario y servidor de correo, y un servidor proxy. Se explica cómo clonar una máquina virtual de referencia para crear los servidores virtuales, configurar sus redes virtuales y tarjetas de red, e instalar Active Directory en el controlador de dominio principal.
The document discusses regression analysis and modeling. It explains that regression analysis allows fitting a straight line through data points to mathematically describe relationships. Models can be used to assess relationships and make predictions. The goals of econometric modeling are to estimate parameters in the model from available data using techniques like ordinary least squares, and to test hypotheses about the parameters. The document provides an example of interpreting regression coefficients from a study on physician compensation.
1) The document discusses how functional diversity decreases with increased land use intensity and agricultural intensification across taxonomic groups. Forest fragments and areas with live fences had greater extinction of species compared to pasture lands.
2) It examines how functional redundancy within taxonomic groups is lost due to land use change. As intensity increases, the number of species performing key functions decreases.
3) The study of agrobiodiversity and human nutrition is presented as a way to consider both sustainable development and theoretical ecology. Research in a region of Kenya found higher on-farm species richness and functional diversity were correlated with improved provision of nutrients important for human health.
The document discusses measures of dispersion such as variance, standard deviation, and the coefficient of variation. It defines variance as the average squared deviation from the mean and standard deviation as the positive square root of the variance. The coefficient of variation measures relative dispersion by dividing the standard deviation by the mean. It is unit-free and allows for comparison across distributions. The document also covers Chebyshev's inequality and how it relates to the proportion of data within a given number of standard deviations from the mean.
The average value of a function f(x) over an interval (a,b) can be approximated as:
f(x) = (f(x1) + f(x2) + ... + f(xn))/n, where x1, x2, ..., xn are values in the interval.
The Fourier coefficients for a periodic function f(x) are:
a0 = (1/π) ∫ f(x) dx
an = (2/π) ∫ f(x) cos(nx) dx
bn = (2/π) ∫ f(x) sin(nx) dx
The Fourier series expansion of
This document discusses hidden Markov models and sequence data. It defines sequence data as ordered sets of elements where the order is determined by time or position. Examples of sequence data include speech, language, bioinformatics data, and time series data. The document introduces graphical models, Bayesian networks, mixture models, and the Markov assumption. It describes hidden Markov models as having hidden states and observations, where the probability of observations depends on the hidden states. Hidden Markov models can model sequential data and problems like evaluation, decoding, and training are discussed.
This document contains solutions to exercises from a pre-calculus textbook on radical functions.
1) It provides tables, graphs and explanations for various radical functions such as √x, √x+3, and their relation to other functions.
2) Students are asked to sketch graphs of radical functions based on given quadratic, cubic or other functions, and identify domains and ranges.
3) Radical equations are solved by graphing related functions and finding the x-intercept(s).
The document discusses calculating volumes of solids of revolution. It provides examples of finding the volume when revolving common shapes around different axes, including:
1) Revolving a cone around the x-axis between a and b to get V = πr2h/3
2) Revolving a sphere of radius r around the x or y-axis to get V = 4/3πr3
3) Revolving y = x2 around the y-axis between 0 and 1 to get V = π/2 units3
It also discusses the general formulas for finding volumes of revolution around the x or y-axis. Examples are accompanied by step-by-step
1) The document discusses calculating volumes of solids formed by rotating areas bounded by graphs around axes.
2) Formulas are provided to calculate volumes when rotating around the x-axis (V = π ∫y2 dx) or y-axis (V = π ∫x2 dy).
3) Examples are worked out for rotating a cone around the x-axis and a sphere around both axes to derive their volume formulas.
1) The document discusses session types in Abelian logic. It introduces primitives for synchronous communication and shows how to represent channels as session types using macros.
2) It proposes adding exchange laws to typed lambda calculus with session types in order to represent commutativity. This results in a system called Abelian logic that is sound and complete.
3) The document considers adding an "eval-subst" rule to allow evaluation of processes with nested channel pairs that would otherwise be deadlocked. This raises issues with preserving types during evaluation that require further formalization.
- The document discusses scalar products and orthogonality in vector spaces.
- It defines the scalar product of two vectors as the sum of the products of their corresponding components.
- Two vectors are orthogonal if their scalar product is equal to 0. Orthogonality can be thought of as a generalization of perpendicularity.
- Several examples are provided to demonstrate calculating scalar products and determining orthogonality in R2 and R3.
Johan Suykens: "Models from Data: a Unifying Picture" ieee_cis_cyprus
The document discusses models that are constructed from data using machine learning techniques. It provides examples of different model types, including neural networks, support vector machines, kernel methods, and spectral clustering. These models can be expressed in both primal and dual formulations, and the dual representations allow for out-of-sample extensions, model selection, and solving large-scale problems. The document outlines core models that underlie many machine learning algorithms and how adding regularization terms and constraints can yield different optimal model representations.
This document discusses probability distributions and some key concepts:
1. It describes discrete and continuous random variables and examples like the binomial, Poisson, and normal distributions.
2. For discrete random variables, it explains how to calculate probabilities, mean, and standard deviation from a probability distribution table.
3. An example is provided to demonstrate calculating these values from data on the number of vehicles owned by households.
4. It also introduces continuous random variables and density functions, noting that the probability of any single value is zero due to the infinite number of possible outcomes. The area under the density function curve represents probabilities.
The document discusses calculating volumes of solids of revolution. It provides examples of finding the volume when revolving common shapes around different axes, including:
1) Revolving a cone around the x-axis between a and b, giving a volume of πmr2h/3.
2) Revolving a sphere of radius r around the x or y-axis, giving a volume of 4/3πr3.
3) Revolving the curve y=x2 around the y-axis between 0 and 1, giving a volume of π/2 units3.
4) Revolving the region under y=5x and above the x-axis between 0
The document discusses several topics in natural language processing including distributional semantics, language models, word embeddings, and neural network models like word2vec. It introduces techniques for distributional semantics using distributional properties of words from large datasets. Language models are discussed including n-gram models and language class models that incorporate word classes. Word embedding techniques like word2vec are introduced for generating word vectors using neural networks.
1. The document provides examples and explanations for solving various types of inequalities involving quadratic equations. It examines cases where a quadratic expression is less than, greater than or equal to zero.
2. Step-by-step workings are shown to arrive at the solution sets for each inequality. Roots of the auxiliary equations are used to determine boundaries for the ranges of values satisfying the inequalities.
3. Assumptions may be made in some cases to simplify the inequalities before determining the final solution sets. Multiple cases are considered to thoroughly address problems involving inequalities of quadratic expressions.
The document contains 17 multiple choice questions about graphing functions and interpreting graphs. Question 1 asks which graph represents y=x^2+2x-3. Question 2 asks to find the value of n+k given a point (k,16) on the graph y=x^n+8. Question 3 asks to find the value of h+k given the graph y=x^2-3x-10.
This document discusses self-organizing neural networks, including Kohonen networks and Adaptive Resonance Theory (ART). It provides details on Kohonen networks such as their basic structure, learning algorithm using neighborhoods, and biological origins. ART is introduced as a way to address the stability-plasticity dilemma in neural networks. The key aspects of ART1 are summarized, including its orienting and attentional subsystems, short and long term memory representations, and learning algorithm using a vigilance test. Examples of a Kohonen network and ART1 network are also included to illustrate their operation.
Los mapas autoorganizativos (SOFM) son redes neuronales que aprenden a clasificar vectores de entrada en grupos similares. La red determina la neurona ganadora más cercana al vector de entrada y actualiza los pesos de esa neurona y sus vecinas para que se asemejen más al vector de entrada. Esto causa que las neuronas vecinas aprendan vectores similares y la red se autoorganice para clasificar uniformemente el espacio de entrada. Varias técnicas como reducir gradualmente el tamaño del vecindario y el índice de aprend
Este documento describe los mapas autorganizativos y el algoritmo de Kohonen. Los mapas autorganizativos realizan aprendizaje no supervisado para representar datos de entrada de alta dimensionalidad en una red de baja dimensionalidad. El algoritmo de Kohonen itera sobre los datos de entrada y ajusta los pesos de la unidad ganadora y sus vecinas para que se parezcan más al dato de entrada. Esto mapea datos similares a unidades adyacentes en la red.
This document describes a self-organizing neural system called ART-TEXTURE that is developed to categorize and classify textured image regions. ART-TEXTURE specializes existing FCD and ART models to achieve high competence in classifying textured scenes without unnecessary mechanisms. As the properties of its component models are "emergent" due to interactions, ART-TEXTURE exhibits new emergent properties for texture classification that are more than just the sum of its parts.
This document discusses self-organizing neural networks, including Kohonen networks and Adaptive Resonance Theory (ART). Kohonen networks use competitive learning to form topological mappings between input and output layers. Neighboring units respond to similar inputs, and learning updates weights of both the winning unit and its neighbors. ART networks learn stable recognition codes in response to input sequences and address the stability-plasticity dilemma by resetting matches that fail a vigilance test.
El documento describe la red neuronal Kohonen, que tiene la capacidad de formar mapas topológicos de las características de entrada similar a como el cerebro representa información. La red Kohonen aprende de forma no supervisada para clasificar patrones de entrada en grupos basados en su similitud, asignando cada grupo a una neurona de salida. El aprendizaje modifica los pesos de las conexiones para que los patrones similares activen neuronas cercanas en la capa de salida.
Este documento describe la teoría de resonancia adaptativa y las redes ART. Explica que las redes ART resuelven el dilema de la estabilidad y plasticidad del aprendizaje mediante un mecanismo de realimentación entre las capas de entrada y salida. Describe la arquitectura básica de una red ART, la cual incluye un subsistema de atención para clasificación y uno de orientación para crear nuevas categorías. También resume diversas adaptaciones de las redes ART desarrolladas para diferentes aplicaciones como el reconocimiento de patrones.
Este documento describe el funcionamiento de una red neuronal artificial con 4 neuronas de entrada y 2 de salida para clasificar patrones binarios. Se inicializan los pesos de las conexiones y se aplican 3 vectores de entrada como ejemplos. Luego, se actualizan los pesos a medida que la red clasifica los patrones de entrada iterativamente.
Este documento describe el Modelo de Resonancia Adaptativa (ART) creado por Stephen Grossberg para permitir que las redes neurales aprendan nuevos patrones de manera plástica mientras retienen patrones previamente aprendidos de forma estable. El modelo ART utiliza una competición entre neuronas para categorizar los patrones de entrada y ajustar los pesos de la red para mejorar la categorización.
Adaptive Resonance Theory (ART) is an unsupervised neural network designed to overcome the stability-plasticity dilemma. ART networks can dynamically classify input data into stable clusters while remaining plastic to learn new clusters. ART-1 specifically handles binary input vectors using a fast, self-organizing hypothesis testing cycle between short-term memory layers F1 and F2. The vigilance parameter controls how closely top-down expectations from F2 must match bottom-up input patterns from F1 before F2 resets and the cycle repeats to find a better match.
La teoría de resonancia adaptativa propone que las redes neuronales pueden aprender nueva información sin olvidar lo aprendido anteriormente mediante la adición de un mecanismo de realimentación entre la capa de entrada y la capa competitiva. La red ART logra esto al alcanzar un estado resonante entre las capas que permite el aprendizaje solo cuando se reconoce rápidamente la entrada, o cuando la entrada es desconocida para crear una nueva representación.
Este documento presenta una introducción al neocognitrón, una arquitectura de red neuronal artificial propuesta para el reconocimiento de caracteres escritos a mano. El neocognitrón se basa en la organización jerárquica de la corteza visual y consta de múltiples niveles de células simples y complejas. Las células simples extraen características de la capa inferior y las células complejas integran las respuestas de grupos de células simples. El neocognitrón es capaz de reconocer caracteres independientemente de
El documento describe la arquitectura y funcionamiento del neocognitrón, una red neuronal concebida para el reconocimiento de caracteres escritos a mano. El neocognitrón tiene una estructura jerárquica compuesta de capas S y C. Las capas S buscan características visuales básicas mientras que las capas C combinan dichas características. El aprendizaje se realiza mediante ajuste de pesos sin supervisión entre representantes de cada capa. La red resuelve ambigüedades mediante inhibición lateral y reconoce múltiples
The document provides biographical information about Professor Kunihiko Fukushima, a pioneer in the field of neural networks. It describes his invention of the Neocognitron, a hierarchical neural network for deformation invariant pattern recognition. The Neocognitron is able to recognize patterns that have been distorted through partial shifts, rotations, or other transformations. The document also discusses Fukushima's research interests in modeling neural networks to understand visual processing and active vision in the brain.
- In 1975, Kunihiko Fukushima introduced the Cognitron network, which was an extension of the original perceptron and was able to handle pattern recognition problems better than the perceptron.
- The Cognitron used multiple layers of convergent subcircuits that allowed it to discriminate between patterns to some degree, unlike the perceptron.
- Fukushima later modified the Cognitron into the Neocognitron in 1980 by adding additional summation nodes, which made the network able to recognize patterns regardless of their position in the visual field.
The counterpropagation network consists of three layers - an input layer, a hidden Kohonen layer, and an output Grossberg layer. The Kohonen layer uses competitive learning to categorize input patterns in an unsupervised manner. During operation, the input pattern activates a single node in the Kohonen layer, which then activates the appropriate output pattern in the Grossberg layer. Effectively, the counterpropagation network acts as a lookup table to map input patterns to associated output patterns by determining which stored pattern category the input belongs to.
The CounterPropagation algorithm updates a neural network with an input, hidden, and output layer. It identifies the hidden neuron with the highest input, setting its activation to 1 and others to 0. The output is then calculated as the weighted sum of the hidden neuron, equal to the weight of the link between the winner hidden neuron and the output neurons. This update works with the CounterPropagation learning function to train the network.
La Counterpropagation es una red neuronal que combina aprendizaje supervisado y no supervisado para acelerar el proceso de aprendizaje. Consiste en dos subredes: una red competitiva de Kohonen para la capa oculta, y una red OUTSTAR para conectar la capa oculta a la de salida. El entrenamiento ocurre en dos fases, primero dividiendo los patrones en clusters y luego ajustando los pesos entre las capas oculta y de salida. Esto permite clasificar nuevos patrones más rápido que las redes multicapa entrenadas solo
La red ART2 es una versión continua del modelo ART original propuesto en 1987 que puede clasificar vectores de entrada reales. Funciona con valores de entrada analógicos manteniendo la misma arquitectura que ART1 pero con pesos iguales. Se utiliza para reconocimiento de imágenes, señales y olores. ARTMAP es una arquitectura supervisada que crea categorías estables optimizando la compresión de códigos y minimizando errores predictivos. Se ha aplicado en diagnóstico médico mejorando la atención de emergencia.
La Constitución de los Estados Unidos establece los principios fundamentales del gobierno federal y garantiza ciertos derechos civiles. El Artículo 1 establece el poder legislativo y crea el Congreso de los Estados Unidos, que se compone de una Cámara de Representantes y un Senado.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
1. Enlarging the Margins in Perceptron
Decision Trees
Kristin P. Bennett, Donghui Wu
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
bennek@rpi.edu, wud2@rpi.edu
Nello Cristianini John Shawe-Taylor
Dept of Engineering Mathematics Dept of Computer Science
University of Bristol Royal Holloway, University of London
nello.cristianini@bristol.ac.uk jst@dcs.rhbnc.ac.uk
0-0
2. Perceptron Decision Trees
Definition 0.1 Perceptron Decision Trees (PDT), are decision
trees in which each internal node is associated with a hyperplane in
general position in the input space, i.e. the decision is constructed
using a linear combination of attributes, instead of one attribute.
w1 x x x x
x x x
x x w3
w1 x
o
x o o o
o o o o
x o
w2 w3 x o o
x o
x o
o o o
x x
x o o x x
w2
1
3. Which Decision Is Better?
– Capacity Control of Linear Classifier
Construct a linear classifier: f (x) = wT x − b, i.e.
find a vector w ∈ Rn and a scalar b such that
f (xi ) = wT xi − b ≥1 if yi = 1,
f (xi ) = wT xi − b ≤ −1 if yi = −1,
i = 1, . . . ,
2
4. Large Margin PDTs Generalize Better
Theorem 0.1 Suppose we are able to classify an m sample of
labeled examples using a perception decision tree and suppose that
the tree obtained contained K decision nodes with margins γi at
node i, then we can bound the generalization error with probability
greater than 1 − δ to be less than
130R2 (4m)K+1 2K
K
D log(4em) log(4m) + log
m (K + 1)δ
K 1
where D = i=1 γi .
2
3
5. The Baseline Algorithms for Comparison
Algorithm 0.1 (Basic OC1 Algorithm ) Start with the root
node, while a node remains to split
• Optimize the decision based on some splitting criterion.
– Randomized search for local minimum.
– Re-starts to jump out of local minimum.
• Partition the node into two or more child nodes based on
decision.
Prune the tree if necessary.
Splitting Criterion : Twoing Rule (goodness measure)
k 2
|TL | |TR | |Li| |Ri |
T woingV alue = ∗ ∗ −
n n i=1
|TL | |TR |
4
6. Twoing Rule
Splitting criteria - Twoing Rule: (Breiman, et al. (1984))
k 2
|TL | |TR | |Li| |Ri |
T woingV alue = ∗ ∗ −
n n i=1
|TL | |TR |
where
n = |TL | + |TR | - total number of instances at current node
k - number of classes, for two class problems
|TL | - number of instances on the left of the split, i.e. wT x − b >= 0
|TR | - number of instances on the right of the split i.e. wT x − b < 0
|Li | - number of instances in category i on the the left of the split
|Ri | - number of instances in category i on the the right of the split
5
7. Enlarging the Margins of PDT
Algorithms of producing large margin PDTs:
• Post-process existing trees (FAT).
Find optimal separating hyperplane at each node of the
existing trees.
• Incorporate large Margin into splitting criteria (MOC1)
max T woingV alue + C ∗ CurrentM argin
• Incorporate large margin into goodness measure (MOC2)
Modified Towing Rule.
6
8. The OC1-PDT and FAT-PDT
IDEA: Post-process the existing OC1-PDT, replace the the OC1
decision with optimal separating hyperlane at each decision node.
x o o o o
x
o o o o
o x x
x x o
x x
x x x
x
x x
x x
x
x x x
o
x o
; x
o
x
o
o OC1
o o
FAT
o
o x
o
7
9. The FAT Algorithm
1. Construct a decision tree using OC1, call it OC1-PDT.
2. Starting from root of OC1-PDT, traverses through all the non-leaf
nodes. At each node,
• Relabel the points at node with ω T x − b ≥ 0 as superclass right,
the other points at this node as superclass left.
• Find the perceptron (optimal separating hyperplane)
f (x) = ω ∗ T x − b∗ , which separates superclasses right and left
perfectly with maximal margin.
• Replace the original perceptron with the new one.
8
10. FAT Generalizes Better Than OC1
10−fold cross validation results: FAT vs OC1
100
95 significant
x=y
90
FAT 10−CV average accuracy
85
80
75
70
65
65 70 75 80 85 90 95 100
OC1 10−CV average accuracy
9
11. MOC1: Margin OC1
IDEA: Use Multi-objective splitting criterion to maximize both
TwoingValue and margin.
max T woingV alue + C ∗ CurrentM argin
x
o
x o
x o
o
x o o
x o
x o
o
10
12. MOC1 Generalizes Better Than OC1
10−fold cross validation results: MOC1 vs OC1
100
significant
not significant
95 x=y
90
MOC1 10−CV average accuracy
85
80
75
70
65
65 70 75 80 85 90 95 100
OC1 10−CV average accuracy
11
13. The MOC2 Algorithm
IDEA: Modify Twoing Criterion to allow “soft-margin”.
Want both high accuracy and strong separation/margin.
k k
|M TL | |M TR | |Li | |Ri | |M Li | |M Ri |
T woingV alue = ∗ ∗ − ∗ −
n n |TL | |TR | |M TL | |M TR |
i=1 i=1
x x o
x x o
x o
x
o o
x
x x x x o
x o o
o o
x x o o o
x o o
x x o o
x x
o
o
x o
x o
x
wx=b+1 wx = b wx=b-1
12
14. The Modified Twoing Rule
k k
|M TL | |M TR | |Li | |Ri | |M Li | |M Ri |
T woingV alue = ∗ ∗ − ∗ −
n n |TL | |TR | |M TL | |M TR |
i=1 i=1
where n = |TL | + |TR | - total number of instances at current node
k - number of classes, for two class problems
|TL | - number of instances on the left of the split, i.e. wT x − b >= 0
|TR | - number of instances on the right of the split i.e. wT x − b < 0
|Li | - number of instances in category i on the the left of the split
|Ri | - number of instances in category i on the the right of the split
|M TL | - number of instances on the left of the split, wT x − b >= 1
|M TR | - number of instances on the right of the split wT x − b <= −1
|M Li | - number of instances in category i with wT x − b >= 1
|M Ri | - number of instances in category i with wT x − b <= −1
13
15. MOC2 Generalizes Better Than OC1
10−fold cross validation results: MOC2 vs OC1
100
significant
95
not significant
x=y
90
MOC2 10−CV average accuracy
85
80
75
70
65
65 70 75 80 85 90 95 100
OC1 10−CV average accuracy
14
17. Conclusions
• Generalization error of PDT is bounded by function of
margins, tree size, and training set size.
• Three algorithms to control capacity of PDT investigated:
– Post-processing existing trees (FAT)
– Incorporating margins into splitting criteria:
∗ Multicriteria splitting rule (MOC1)
∗ Soft-margin modified twoing-rule (MOC2).
• Theoretically and empirically enlarged margin PDT performed
better.
16