A deep belief network (DBN) is a probabilistic generative model formed by stacking multiple restricted Boltzmann machines (RBMs). RBMs are shallow neural networks that extract meaningful features from input data in the forward pass and attempt to reconstruct the input in the backward pass. A DBN divides the network into multiple RBM layers for unsupervised pre-training followed by a feedforward backpropagation network for fine-tuning. This training process helps overcome issues with training deep networks from scratch using backpropagation alone such as slow convergence and getting stuck in poor local optima.
Analysis and design of algorithms part 4Deepak John
Complexity Theory - Introduction. P and NP. NP-Complete problems. Approximation algorithms. Bin packing, Graph coloring. Traveling salesperson Problem.
Show ant-colony-optimization-for-solving-the-traveling-salesman-problemjayatra
The document describes using ant colony optimization to solve the traveling salesman problem. It outlines the traveling salesman problem and introduces ant colony optimization as a metaheuristic for solving optimization problems inspired by ant behavior. The document then provides an example of using ant colony optimization to iteratively find the shortest route between 5 cities, with ants probabilistically choosing paths based on pheromone levels and distance.
This document provides an overview of graph representation learning and various methods for learning embeddings of nodes in graph-structured data. It introduces shallow methods like DeepWalk and Node2Vec that learn embeddings by generating random walks. It then discusses deep methods like graph convolutional networks (GCN) and GraphSAGE that learn embeddings through neural network aggregation of node neighborhoods. Graph attention networks are also introduced as a learnable aggregator for GCN. Finally, applications of these methods at Pinterest for pin recommendation and at Uber Eats for dish recommendation are briefly described.
This document provides an introduction to k-means clustering, including:
1. K-means clustering aims to partition n observations into k clusters by minimizing the within-cluster sum of squares, where each observation belongs to the cluster with the nearest mean.
2. The k-means algorithm initializes cluster centroids and assigns observations to the nearest centroid, recomputing centroids until convergence.
3. K-means clustering is commonly used for applications like machine learning, data mining, and image segmentation due to its efficiency, though it is sensitive to initialization and assumes spherical clusters.
Why should you care about Markov Chain Monte Carlo methods?
→ They are in the list of "Top 10 Algorithms of 20th Century"
→ They allow you to make inference with Bayesian Networks
→ They are used everywhere in Machine Learning and Statistics
Markov Chain Monte Carlo methods are a class of algorithms used to sample from complicated distributions. Typically, this is the case of posterior distributions in Bayesian Networks (Belief Networks).
These slides cover the following topics.
→ Motivation and Practical Examples (Bayesian Networks)
→ Basic Principles of MCMC
→ Gibbs Sampling
→ Metropolis–Hastings
→ Hamiltonian Monte Carlo
→ Reversible-Jump Markov Chain Monte Carlo
k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells.
A deep belief network (DBN) is a probabilistic generative model formed by stacking multiple restricted Boltzmann machines (RBMs). RBMs are shallow neural networks that extract meaningful features from input data in the forward pass and attempt to reconstruct the input in the backward pass. A DBN divides the network into multiple RBM layers for unsupervised pre-training followed by a feedforward backpropagation network for fine-tuning. This training process helps overcome issues with training deep networks from scratch using backpropagation alone such as slow convergence and getting stuck in poor local optima.
Analysis and design of algorithms part 4Deepak John
Complexity Theory - Introduction. P and NP. NP-Complete problems. Approximation algorithms. Bin packing, Graph coloring. Traveling salesperson Problem.
Show ant-colony-optimization-for-solving-the-traveling-salesman-problemjayatra
The document describes using ant colony optimization to solve the traveling salesman problem. It outlines the traveling salesman problem and introduces ant colony optimization as a metaheuristic for solving optimization problems inspired by ant behavior. The document then provides an example of using ant colony optimization to iteratively find the shortest route between 5 cities, with ants probabilistically choosing paths based on pheromone levels and distance.
This document provides an overview of graph representation learning and various methods for learning embeddings of nodes in graph-structured data. It introduces shallow methods like DeepWalk and Node2Vec that learn embeddings by generating random walks. It then discusses deep methods like graph convolutional networks (GCN) and GraphSAGE that learn embeddings through neural network aggregation of node neighborhoods. Graph attention networks are also introduced as a learnable aggregator for GCN. Finally, applications of these methods at Pinterest for pin recommendation and at Uber Eats for dish recommendation are briefly described.
This document provides an introduction to k-means clustering, including:
1. K-means clustering aims to partition n observations into k clusters by minimizing the within-cluster sum of squares, where each observation belongs to the cluster with the nearest mean.
2. The k-means algorithm initializes cluster centroids and assigns observations to the nearest centroid, recomputing centroids until convergence.
3. K-means clustering is commonly used for applications like machine learning, data mining, and image segmentation due to its efficiency, though it is sensitive to initialization and assumes spherical clusters.
Why should you care about Markov Chain Monte Carlo methods?
→ They are in the list of "Top 10 Algorithms of 20th Century"
→ They allow you to make inference with Bayesian Networks
→ They are used everywhere in Machine Learning and Statistics
Markov Chain Monte Carlo methods are a class of algorithms used to sample from complicated distributions. Typically, this is the case of posterior distributions in Bayesian Networks (Belief Networks).
These slides cover the following topics.
→ Motivation and Practical Examples (Bayesian Networks)
→ Basic Principles of MCMC
→ Gibbs Sampling
→ Metropolis–Hastings
→ Hamiltonian Monte Carlo
→ Reversible-Jump Markov Chain Monte Carlo
k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells.
The document discusses various algorithm design techniques, including brute force. It describes brute force as the simplest approach that directly solves a problem based on its definition. While brute force is widely applicable and simple, its algorithms tend to be inefficient. Examples given of brute force algorithms include selection sort, string matching, and exhaustive search. Selection sort is then explained in more detail, along with pseudocode. Brute force string matching is also explained, with pseudocode provided.
Neural networks can be biological models of the brain or artificial models created through software and hardware. The human brain consists of interconnected neurons that transmit signals through connections called synapses. Artificial neural networks aim to mimic this structure using simple processing units called nodes that are connected by weighted links. A feed-forward neural network passes information in one direction from input to output nodes through hidden layers. Backpropagation is a common supervised learning method that uses gradient descent to minimize error by calculating error terms and adjusting weights between layers in the network backwards from output to input. Neural networks have been applied successfully to problems like speech recognition, character recognition, and autonomous vehicle navigation.
This was a presentation done for the Techspace of IoT Asia 2017 oon 30th March 2017. This is an introductory session to introduce the concept of Long Short-Term Memory (LSTMs) for the prediction in Time Series. I also shared the Keras code to work out a simple Sin Wave example and a Household power consumption data to use for the predictions. The links for the code can be found in the presentation.
In computer science and operation research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graph.
This document introduces graph neural networks and discusses a claim that they are essentially low-pass filters. It provides an overview of graph neural network operations, including combining node features, aggregating information from neighbors, and updating node representations over multiple layers. The document notes that while graph neural networks may be less powerful than other deep learning methods, they are interesting for problems involving graphs, such as drug discovery and web analytics. It questions how graph neural network classifications operate and whether the low-pass filter behavior is caused by the graph Laplacian matrix.
Slides for a talk about Graph Neural Networks architectures, overview taken from very good paper by Zonghan Wu et al. (https://arxiv.org/pdf/1901.00596.pdf)
This document describes DenseNets, a type of convolutional neural network architecture. DenseNets connect each layer to every other layer in a feed-forward fashion to encourage feature reuse and consolidate feature maps early in the network. This architecture improves information and gradient flow. The document outlines key DenseNet concepts like collective knowledge, compression layers, and growth rate. It also provides results comparing DenseNets to ResNet on CIFAR-10 and ImageNet datasets.
The document discusses K-means clustering and DBSCAN, two popular clustering algorithms. K-means clusters data by minimizing distances between points and cluster centroids. It works by iteratively assigning points to the closest centroid and recalculating centroids. DBSCAN clusters based on density rather than distance; it identifies dense regions separated by sparse regions to form clusters without specifying the number of clusters.
This document discusses independent component analysis (ICA) for blind source separation. ICA is a method to estimate original signals from observed signals consisting of mixed original signals and noise. It introduces the ICA model and approach, including whitening, maximizing non-Gaussianity using kurtosis and negentropy, and fast ICA algorithms. The document provides examples applying ICA to separate images and discusses approaches to improve ICA, including using differential filtering. ICA is an important technique for blind source separation and independent component estimation from observed signals.
The document provides an introduction to Markov Chain Monte Carlo (MCMC) methods. It discusses using MCMC to sample from distributions when direct sampling is difficult. Specifically, it introduces Gibbs sampling and the Metropolis-Hastings algorithm. Gibbs sampling updates variables one at a time based on their conditional distributions. Metropolis-Hastings proposes candidate samples and accepts or rejects them to converge to the target distribution. The document provides examples and outlines the algorithms to construct Markov chains that sample distributions of interest.
This presentation is intended for giving an introduction to Genetic Algorithm. Using an example, it explains the different concepts used in Genetic Algorithm. If you are new to GA or want to refresh concepts , then it is a good resource for you.
This document discusses the K-nearest neighbors (KNN) algorithm, an instance-based learning method used for classification. KNN works by identifying the K training examples nearest to a new data point and assigning the most common class among those K neighbors to the new point. The document covers how KNN calculates distances between data points, chooses the value of K, handles feature normalization, and compares strengths and weaknesses of the approach. It also briefly discusses clustering, an unsupervised learning technique where data is grouped based on similarity.
This document discusses soft computing techniques. Soft computing deals with inexact solutions and uses techniques like fuzzy systems, neural networks, machine learning, and probabilistic reasoning. It summarizes the key differences between hard and soft computing, providing examples of each technique. The document concludes by listing some common applications of soft computing such as handwriting recognition, image processing, and decision support systems.
The ArangoML Group had a detailed discussion on the topic "GraphSage Vs PinSage" where they shared their thoughts on the difference between the working principles of two popular Graph ML algorithms. The following slidedeck is an accumulation of their thoughts about the comparison between the two algorithms.
References:
"Gaussian Process", Lectured by Professor Il-Chul Moon
"Gaussian Processes", Cornell CS4780 , Lectured by Professor
Kilian Weinberger
Bayesian Deep Learning by Sungjoon Choi
K-means clustering is an algorithm that groups data points into k clusters based on their attributes and distances from initial cluster center points. It works by first randomly selecting k data points as initial centroids, then assigning all other points to the closest centroid and recalculating the centroids. This process repeats until the centroids are stable or a maximum number of iterations is reached. K-means clustering is widely used for machine learning applications like image segmentation and speech recognition due to its efficiency, but it is sensitive to initialization and assumes spherical clusters of similar size and density.
In this tutorial, we will learn the the following topics -
+ Linear SVM Classification
+ Soft Margin Classification
+ Nonlinear SVM Classification
+ Polynomial Kernel
+ Adding Similarity Features
+ Gaussian RBF Kernel
+ Computational Complexity
+ SVM Regression
k Nearest Neighbor (kNN) is a simple machine learning algorithm that classifies new data based on the majority class of its k nearest neighbors. kNN has been used since the 1970s for statistical estimation and pattern recognition. It can be used for classification or regression tasks in fields like text mining, agriculture, finance, and healthcare. The distance between data points, usually Euclidean distance, is used to find the k nearest neighbors. kNN performance depends on selecting an optimal value for k through cross-validation. Normalizing input variables and increasing training data size can improve kNN accuracy.
Topological Data Analysis and Persistent HomologyCarla Melia
This document provides an overview of topological data analysis and persistent homology. It discusses how topological data analysis uses techniques from fields like statistics, computer science, and algebraic topology to infer robust features about complex datasets. Persistent homology in particular analyzes the homology of filtrations to study topological features across different scales. The document also describes implementations of topological data analysis techniques and applications to areas such as brain networks, periodic systems, and cosmological data analysis.
The document provides an introduction to graph theory. It lists prescribed and recommended books, outlines topics that will be covered including history, definitions, types of graphs, terminology, representation, subgraphs, connectivity, and applications. It notes that the Government of India designated June 10th as Graph Theory Day in recognition of the influence and importance of graph theory.
The document discusses various algorithm design techniques, including brute force. It describes brute force as the simplest approach that directly solves a problem based on its definition. While brute force is widely applicable and simple, its algorithms tend to be inefficient. Examples given of brute force algorithms include selection sort, string matching, and exhaustive search. Selection sort is then explained in more detail, along with pseudocode. Brute force string matching is also explained, with pseudocode provided.
Neural networks can be biological models of the brain or artificial models created through software and hardware. The human brain consists of interconnected neurons that transmit signals through connections called synapses. Artificial neural networks aim to mimic this structure using simple processing units called nodes that are connected by weighted links. A feed-forward neural network passes information in one direction from input to output nodes through hidden layers. Backpropagation is a common supervised learning method that uses gradient descent to minimize error by calculating error terms and adjusting weights between layers in the network backwards from output to input. Neural networks have been applied successfully to problems like speech recognition, character recognition, and autonomous vehicle navigation.
This was a presentation done for the Techspace of IoT Asia 2017 oon 30th March 2017. This is an introductory session to introduce the concept of Long Short-Term Memory (LSTMs) for the prediction in Time Series. I also shared the Keras code to work out a simple Sin Wave example and a Household power consumption data to use for the predictions. The links for the code can be found in the presentation.
In computer science and operation research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graph.
This document introduces graph neural networks and discusses a claim that they are essentially low-pass filters. It provides an overview of graph neural network operations, including combining node features, aggregating information from neighbors, and updating node representations over multiple layers. The document notes that while graph neural networks may be less powerful than other deep learning methods, they are interesting for problems involving graphs, such as drug discovery and web analytics. It questions how graph neural network classifications operate and whether the low-pass filter behavior is caused by the graph Laplacian matrix.
Slides for a talk about Graph Neural Networks architectures, overview taken from very good paper by Zonghan Wu et al. (https://arxiv.org/pdf/1901.00596.pdf)
This document describes DenseNets, a type of convolutional neural network architecture. DenseNets connect each layer to every other layer in a feed-forward fashion to encourage feature reuse and consolidate feature maps early in the network. This architecture improves information and gradient flow. The document outlines key DenseNet concepts like collective knowledge, compression layers, and growth rate. It also provides results comparing DenseNets to ResNet on CIFAR-10 and ImageNet datasets.
The document discusses K-means clustering and DBSCAN, two popular clustering algorithms. K-means clusters data by minimizing distances between points and cluster centroids. It works by iteratively assigning points to the closest centroid and recalculating centroids. DBSCAN clusters based on density rather than distance; it identifies dense regions separated by sparse regions to form clusters without specifying the number of clusters.
This document discusses independent component analysis (ICA) for blind source separation. ICA is a method to estimate original signals from observed signals consisting of mixed original signals and noise. It introduces the ICA model and approach, including whitening, maximizing non-Gaussianity using kurtosis and negentropy, and fast ICA algorithms. The document provides examples applying ICA to separate images and discusses approaches to improve ICA, including using differential filtering. ICA is an important technique for blind source separation and independent component estimation from observed signals.
The document provides an introduction to Markov Chain Monte Carlo (MCMC) methods. It discusses using MCMC to sample from distributions when direct sampling is difficult. Specifically, it introduces Gibbs sampling and the Metropolis-Hastings algorithm. Gibbs sampling updates variables one at a time based on their conditional distributions. Metropolis-Hastings proposes candidate samples and accepts or rejects them to converge to the target distribution. The document provides examples and outlines the algorithms to construct Markov chains that sample distributions of interest.
This presentation is intended for giving an introduction to Genetic Algorithm. Using an example, it explains the different concepts used in Genetic Algorithm. If you are new to GA or want to refresh concepts , then it is a good resource for you.
This document discusses the K-nearest neighbors (KNN) algorithm, an instance-based learning method used for classification. KNN works by identifying the K training examples nearest to a new data point and assigning the most common class among those K neighbors to the new point. The document covers how KNN calculates distances between data points, chooses the value of K, handles feature normalization, and compares strengths and weaknesses of the approach. It also briefly discusses clustering, an unsupervised learning technique where data is grouped based on similarity.
This document discusses soft computing techniques. Soft computing deals with inexact solutions and uses techniques like fuzzy systems, neural networks, machine learning, and probabilistic reasoning. It summarizes the key differences between hard and soft computing, providing examples of each technique. The document concludes by listing some common applications of soft computing such as handwriting recognition, image processing, and decision support systems.
The ArangoML Group had a detailed discussion on the topic "GraphSage Vs PinSage" where they shared their thoughts on the difference between the working principles of two popular Graph ML algorithms. The following slidedeck is an accumulation of their thoughts about the comparison between the two algorithms.
References:
"Gaussian Process", Lectured by Professor Il-Chul Moon
"Gaussian Processes", Cornell CS4780 , Lectured by Professor
Kilian Weinberger
Bayesian Deep Learning by Sungjoon Choi
K-means clustering is an algorithm that groups data points into k clusters based on their attributes and distances from initial cluster center points. It works by first randomly selecting k data points as initial centroids, then assigning all other points to the closest centroid and recalculating the centroids. This process repeats until the centroids are stable or a maximum number of iterations is reached. K-means clustering is widely used for machine learning applications like image segmentation and speech recognition due to its efficiency, but it is sensitive to initialization and assumes spherical clusters of similar size and density.
In this tutorial, we will learn the the following topics -
+ Linear SVM Classification
+ Soft Margin Classification
+ Nonlinear SVM Classification
+ Polynomial Kernel
+ Adding Similarity Features
+ Gaussian RBF Kernel
+ Computational Complexity
+ SVM Regression
k Nearest Neighbor (kNN) is a simple machine learning algorithm that classifies new data based on the majority class of its k nearest neighbors. kNN has been used since the 1970s for statistical estimation and pattern recognition. It can be used for classification or regression tasks in fields like text mining, agriculture, finance, and healthcare. The distance between data points, usually Euclidean distance, is used to find the k nearest neighbors. kNN performance depends on selecting an optimal value for k through cross-validation. Normalizing input variables and increasing training data size can improve kNN accuracy.
Similar to Learning the structure of Gaussian Graphical models with unobserved variables by Marina Vinyes, Software Engineer in Machine Learning @Criteo
Topological Data Analysis and Persistent HomologyCarla Melia
This document provides an overview of topological data analysis and persistent homology. It discusses how topological data analysis uses techniques from fields like statistics, computer science, and algebraic topology to infer robust features about complex datasets. Persistent homology in particular analyzes the homology of filtrations to study topological features across different scales. The document also describes implementations of topological data analysis techniques and applications to areas such as brain networks, periodic systems, and cosmological data analysis.
The document provides an introduction to graph theory. It lists prescribed and recommended books, outlines topics that will be covered including history, definitions, types of graphs, terminology, representation, subgraphs, connectivity, and applications. It notes that the Government of India designated June 10th as Graph Theory Day in recognition of the influence and importance of graph theory.
This document summarizes Eric Xing's lecture on dimensionality reduction and machine learning. It discusses several techniques for dimensionality reduction including principal component analysis (PCA), locality preserving projections (LLE), and isomap. PCA finds orthogonal directions of maximum variance in high-dimensional data to project it to a lower-dimensional space. LLE and isomap are nonlinear dimensionality reduction techniques that can discover low-dimensional manifold structures. Applications discussed include text retrieval, image analysis, and super resolution image reconstruction. Dimensionality reduction is useful for pattern recognition, information retrieval, and exploring high-dimensional datasets.
This document discusses network representation and analysis. It defines networks as consisting of nodes (vertices) and edges, and describes different ways to represent networks mathematically using adjacency matrices, incidence matrices, and Laplacian matrices. It also discusses visualizing networks using multidimensional scaling and plotting them in R. Special types of networks like complete graphs and random graphs are briefly introduced.
Line graphs, slope, and interpreting line graphs Charalee
The document discusses how to draw and interpret line graphs from data. It provides instructions on properly labeling the axes, plotting data points, and drawing a best-fit line through the points. It also defines slope as the constant in the linear equation y=kx and explains how to calculate slope using the rise over run formula.
Computational Information Geometry: A quick review (ICMS)Frank Nielsen
From the workshop
Computational information geometry for image and signal processing
Sep 21, 2015 - Sep 25, 2015
ICMS, 15 South College Street, Edinburgh
http://www.icms.org.uk/workshop.php?id=343
An elementary introduction to information geometryFrank Nielsen
This document provides an elementary introduction to information geometry. It discusses how information geometry generalizes concepts from Riemannian geometry to study the geometry of decision making and model fitting. Specifically, it introduces:
1. Dually coupled connections (∇, ∇*) that are compatible with a metric tensor g and define dual parallel transport on a manifold.
2. The fundamental theorem of information geometry, which states that manifolds with dually coupled connections (∇, ∇*) have the same constant curvature.
3. Examples of statistical manifolds with dually flat geometry that arise from Bregman divergences and f-divergences, making them useful for modeling relationships between probability distributions
ESWC2015 - Tutorial on Publishing and Interlinking Linked Geospatial DataKostis Kyzirakos
In this tutorial we present the life cycle of linked geospatial data and we focus on two important steps: the publication of geospatial data as RDF graphs and interlinking them with each other. Given the proliferation of geospatial information on the Web many kinds of geospatial data are now becoming available as linked datasets (e.g., Google and Bing maps, user-generated geospatial content, public sector information published as open data etc.). The topic of the tutorial is related to all core research areas of the Semantic Web (e.g., semantic information extraction, transformation of data into RDF graphs, interlinking linked data etc.) since there is often a need to re-consider existing core techniques when we deal with geospatial information. Thus, it is timely to train Semantic Web researchers, especially the ones that are in the early stages of their careers, on the state of the art of this area and invite them to contribute to it.
In this tutorial we give a comprehensive background on data models, query languages, implemented systems for linked geospatial data, and we discuss recent approaches on publishing and interlinking geospatial data. The tutorial is complemented with a hands-on session that will familiarize the audience with the state-of-the-art tools in publishing and interlinking geospatial information.
http://event.cwi.nl/eswc2015-geo/
Information geometry: Dualistic manifold structures and their usesFrank Nielsen
Information geometry: Dualistic manifold structures and their uses
by Frank Nielsen
Talk given at ICML GIMLI2018
http://gimli.cc/2018/
See tutorial at:
https://arxiv.org/abs/1808.08271
``An elementary introduction to information geometry''
This document summarizes the work of Working Group II on Probabilistic Numerics from the SAMSI QMC Transition Workshop. The working group aims to develop probabilistic numerical methods that provide a richer probabilistic quantification of numerical error in outputs, allowing for better statistical inference. Members of the working group have published several papers on topics like Bayesian probabilistic numerical methods for solving differential equations and performing integral approximations, and applying these methods to problems in mathematical epidemiology and industrial process monitoring. The group has also organized workshops and reading groups to discuss the development of probabilistic numerical methods.
Gradient Dynamical Systems, Bifurcation Theory, Numerical Methods and Applica...Boris Fackovec
This document is a presentation on gradient dynamical systems, bifurcation theory, numerical methods, and applications. It discusses dynamical systems, phase portraits, linear and nonlinear systems of ordinary differential equations, bifurcations, bifurcation diagrams, numerical methods for constructing bifurcation diagrams, and two examples - a chemical reactor system and a cluster of three charged atoms.
This document provides a lesson on calculating distances on the coordinate plane. It includes examples of finding the distances between points that lie on the same horizontal or vertical axis, as well as points that form horizontal or vertical line segments not on an axis. Students are given exercises to find the lengths of line segments from their endpoints and word problems involving distances on the coordinate plane. The lesson emphasizes that finding distances between points on the same horizontal or vertical line can be done in the same way as the number line.
The remote sensing working group has investigated methodology for atmospheric remotesensing retrievals, which are mathematical and computational procedures for inferring the state of the atmosphere from remote sensing observations. Satellite data with fine spatial and temporal
resolution present opportunities to combine information across satellite pixels using spatiotemporal statistical modeling. We present examples of this approach at the process level of a hierarchical model, with a nonlinear radiative transfer model incorporated into the likelihood. In
this framework, we assess the impact of various statistical properties on the relative performance of a multi-pixel retrieval strategy versus an operational one-at-a-time approach. The prospect of adopting the approach is illustrated in the context of estimating atmospheric carbon dioxide concentration with data from NASA's Orbiting Carbon Observatory-2 (OCO-2).
The document defines a graph and discusses its history, types, representations, and applications. It begins with Leonhard Euler's solving of the Königsberg bridge problem in 1735, which is considered the first theorem of graph theory. A graph is defined as a pair of sets (V,E) where V is the set of vertices and E is the set of edges. Graphs can have parallel edges, loops, directed or undirected edges. They can be represented through adjacency matrices or lists. Applications of graph theory include computer science, physics/chemistry, and computer networks.
Lecture 07 leonidas guibas - networks of shapes and imagesmustafa sarac
The document discusses extracting shared structure from networks of related images and shapes through joint analysis. It proposes estimating consistent functional maps between images in a network, allowing functions like object segmentations to be transported across images. Estimating functional maps involves preserving features while enforcing cycle consistency across the network. This emerges shared "object functions" representing consistently segmented objects across related images. Experiments on object co-segmentation datasets demonstrate improved segmentation by exploiting relationships in an image network.
Pattern learning and recognition on statistical manifolds: An information-geo...Frank Nielsen
This document provides an overview of Frank Nielsen's talk on pattern learning and recognition using information geometry and statistical manifolds. The talk focuses on departing from vector space representations and dealing with (dis)similarities that do not have Euclidean or metric properties. This poses new theoretical and computational challenges for pattern recognition. The talk describes using exponential family mixture models defined on dually flat statistical manifolds induced by convex functions. On these manifolds, dual coordinate systems and dual affine geodesics allow for computing-friendly representations of divergences and similarities between probabilistic patterns. The techniques aim to achieve statistical invariance and enable algorithmic approaches to problems like Gaussian mixture modeling, shape retrieval, and diffusion tensor imaging analysis.
The document discusses key concepts related to sets. It defines what a set is and the different ways of representing sets. It describes types of sets such as empty, finite, infinite and singleton sets. It explains the concepts of subset, equal sets, power set and different set operations like union, intersection, difference and complement. It provides properties and laws related to these set operations including commutative, associative and De Morgan's laws. It also discusses different types of intervals on the number line.
The document provides information about a faculty development program on discrete mathematics. It includes:
- An outline of the course content which covers topics like graph terminology, representations of graphs, connectivity, Euler and Hamilton paths, shortest path algorithms, planar graphs, and graph coloring.
- Details of learning resources including textbooks and reference books.
- A table listing the topics to be discussed in lectures, related self-learning tasks, reference materials and number of contact hours.
- Information on representation of graphs through adjacency matrix, incidence matrix and adjacency lists.
The program aims to teach key concepts in graph theory and related algorithms over 6 lecture hours through lectures, self-study and reference books.
The boundary element method is used to simulate the flow of an emulsion drop through a converging channel. The drop flow is governed by the Stokes equations since the Reynolds number is low. Integral equations are derived relating the velocity and stress fields on the drop surface and channel boundaries. The equations account for the viscosity ratio, capillary number, and drop shape. Nodes and quadratic elements are used to discretize the boundaries and solve the integral equations numerically. The results show the effect of parameters on the flow rate-pressure relation and drop shape dynamics.
Similar to Learning the structure of Gaussian Graphical models with unobserved variables by Marina Vinyes, Software Engineer in Machine Learning @Criteo (20)
As electricity is difficult to store, it is crucial to strictly maintain the balance between production and consumption. The integration of intermittent renewable energies into the production mix has made the management of the balance more complex. However, access to near real-time data and communication with consumers via smart meters suggest demand response. Specifically, sending signals would encourage users to adjust their consumption according to the production of electricity. The algorithms used to select these signals must learn consumer reactions and optimize them while balancing exploration and exploitation. Various sequential or reinforcement learning approaches are being considered.
Online violence amplifies IRL discriminations, and the lack of diversity grows in a vicious circle. Understanding cyber-violence, its forms and mechanisms, can help us fight back. To process massive volumes of data, AI finally comes into play for good.
In the energy sector, the use of temporal data stands as a pivotal topic. At GRDF, we have developed several methods to effectively handle such data. This presentation will specifically delve into our approaches for anomaly detection and data imputation within time series, leveraging transformers and adversarial training techniques.
Natasha shares her experience to delve into the complexities, challenges, and strategies associated with effectively leading tech teams dispersed across borders.
Nour and Maria present the work they did at Tweag, Modus Create innovation arm, where the GenAI team developed an evaluation framework for Retrieval-Augmented Generation (RAG) systems. RAG systems provide an easy and low-cost way to extend the knowledge of Large Language Models (LLMs) but measuring their performance is not an easy task.
The presentation will review existing evaluation frameworks, ranging from those based on the traditional ML approach of using groundtruth datasets, including Tweag's, to those that use LLMs to compute evaluation metrics.
It will also delve into the practical implementation of Tweag's chatbot over two distinct documents datasets and provide insights on chunking, embedding and how open source and commercial LLMs compare.
Sharone Dayan, Machine Learning Engineer and Daria Stefic, Data Scientist, both from Contentsquare, delve into evaluation strategies for dealing with partially labelled or unlabelled data.
COMPASS is a new framework that trains a latent space of diverse reinforcement learning policies to solve combinatorial optimization problems. It has two phases: (1) training phase samples the latent space and trains policies, and (2) inference phase searches the latent space within a budget to find high-performing policies. COMPASS achieves state-of-the-art results on 29 tasks, generalizes better than baselines on out-of-distribution instances, and its search strategy effectively reaches high-performance regions of the latent space.
Laure talked about a very hot topic in the community at the moment with the ChatGPT phenomenon: how to supervise a PhD thesis in NLP in the age of Large Language Models (LLMs)?
This document describes the journey of building a sales forecasting data product at Maisons du Monde, a large European home goods retailer. It outlines the challenges of forecasting during the COVID pandemic when supply chains were disrupted. The data science team developed forecasting models using techniques like N-Beats and LightGBM and established workflows to generate regular forecasts. Key learnings included the importance of evaluating forecasts against a naive baseline, incorporating external factors, and partnering with business stakeholders who will have the final say in operational forecasts. The project established robust technical foundations to support future forecasting needs.
Abstract: Who hasn't heard of the "Pilot Syndrome"? 85% of Data Science Pilots remain pilots and do not make it to the production stage. Let's build a production-ready and end-user-friendly Data Science application. 100% python and 100% open source.
Phase 1 | Building the GUI: create an interactive and powerful interface in a few lines of code
Phase 2 | Integrated back end: Manage your models and pipelines and create scenarios the smart way
"Nature Language Processing for proteins" by Amélie Héliou, Software Engineer @ Google Research
Abstract: Over the past few months, Large Language Models have become very popular.
We'll see how a simple LLM works, from input sentence to prediction.
I'll then present an application of LLM to protein name prediction.
Twitter: @Amelie_hel
This document discusses the automation of the Bechdel-Wallace test using artificial intelligence. It describes the Bechdel-Wallace test, which evaluates whether a work of fiction features at least two women who talk to each other about something other than a man. The project, called BechdelAI, aims to use AI tools like image recognition, natural language processing, and text analysis to automatically apply the Bechdel-Wallace test to movies and measure gender representation and inequalities in cinema. It outlines initial phases including collecting data from sources like IMDb and OpenSubtitles, visualizing gender breakdowns of casts and crews, analyzing movie posters, and studying relationships between characters based on age gaps.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Learning the structure of Gaussian Graphical models with unobserved variables by Marina Vinyes, Software Engineer in Machine Learning @Criteo
1. Learning the structure of Gaussian
Graphical models with unobserved variables
Marina Vinyes, Ph.D.
Paris WiMLDS Organizer, Machine Learning Engineer at Criteo
4th June 2019
1 / 17
2. Why graphical models?
Graphs are a natural way to represent data
Family tree Social network
Gene regulatory
network
Left: Photo of Marie Curie Museum (Muzeum Marii Sklodowskiej-Curie) is courtesy of TripAdvisor. Middle:
https://en.wikipedia.org/wiki/Social graph. Right: Emmert Streib et al. [2014] 2 / 17
3. What are graphical models?
Nodes correspond to random variables
Edges correspond to statistical dependencies between variables
Different kinds of graphical models
directed/undirected graph
discrete/continous/both variables
3 / 17
4. Conditional independence
B
A C
B: Train strike
A: Marina is late
C: Caroline is late
A and C independent?
No
A and C cond. independent
given B?
Yes
B
A C
B: Traffic jam
A: Rain
C: Football match
A and C independent?
Yes
A and C cond. independent
given B?
No
4 / 17
5. Learning the structure of a graphical model
Goal: Knowledge discovery, first step towards causality effects,. . .
X1
X2 X3
X4
X6 X5
X1
X2 X3
X4
X6 X5
5 / 17
6. Learning the structure of a graphical model
Easier for undirected Gaussian graphical models...
Σ−1
i,j = 0 if and only if no edge between Xi and Xj
(where Σ−1 is the inverse covariance matrix)
X1
X2 X3
X4
X6 X5
ˆΣ−1 ≈
Clarification: All next slides only undirected Gaussian
graphical models
6 / 17
7. Graphical lasso: sparsity assumption
Approximation:
ˆΣ the empirical covariance matrix
ˆΣ−1 ≈ sparse
Formulation:
min
S
fnll (S) + λ S 1
s.t. S 0
Negative log likelihood fnll (M) := − log det(M) + tr(MΣ)
Semidefinite program
7 / 17
8. What if some variables are unobserved?
Consider a graphical model with 2 latent variables
Complete graph, 12 edges
sparse structure
Marginalized graph, 22 edges
not so sparse structure
8 / 17
9. Link with the structure of the precision matrix K
K = Σ−1 where Σ is the covariance of the full graph
X1
X2
X3
X4
X6
X5
X7
X8
X9
X10
X11
Inversion formula: Σ−1
OO = KOO − UK−1
HHU
9 / 17
10. Previous work
Chandrasekaran et al. [2010]
Since, Σ−1
OO = KOO − UK−1
HHU
Approximation:
ˆΣOO the empirical covariance matrix
ˆΣ−1
OO ≈ sparse + low rank
Formulation:
min
S,L
fnll (S − L) + λ(η S 1 + tr(L))
s.t. S − L 0 L 0
Negative log likelihood fnll (M) := − log det(M) + tr(MΣOO)
Semidefinite program
Limitation:
The low rank component does not recover the connectivity
between latent and observed variables
10 / 17
11. Our formulation: more structure on L
Assuming:
latent variables are independent (KHH is diagonal)
every latent variable is connected to k observed variables
ˆΣ−1
OO ≈ sparse + L where we impose structure on L
using an atomic norm on L ≈ UU
min
S,L
fnll (S − L) + λ(η S 1 + γA(L))
s.t. S − L 0 L 0
11 / 17
12. Our formulation: more structure on L
Σ−1
OO ≈ +s1 u1u1 +s2 +s3u2u2 u3u3
S L1 L2 L3
Atomic norm γA:
Atomic norm for matrices [Richard et al., 2014]
A := {uu | u ∈ Rp
: u 0 ≤ k, u 2 = 1}
12 / 17
14. Conclusion and perspectives
convex approach with matrix regularization
real dataset
directed graphs
full paper with algorithm and identifiability results
https://arxiv.org/abs/1807.07754
14 / 17
16. References I
V. Chandrasekaran, P. A. Parrilo, and A. S. Willsky. Latent variable
graphical model selection via convex optimization. In Communication,
Control, and Computing (Allerton), 2010 48th Annual Allerton
Conference on, pages 1610–1613. IEEE, 2010.
V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky. The
convex geometry of linear inverse problems. Foundations of
Computational mathematics, 12(6):805–849, 2012.
F. Emmert Streib, R. De Matos Simoes, P. Mullan, B. Haibe-Kains, and
M. Dehmer. The gene regulatory network for breast cancer: integrated
regulatory landscape of cancer hallmarks. Frontiers in Genetics, 5:15,
2014.
E. Richard, G. R. Obozinski, and J.-P. Vert. Tight convex relaxations for
sparse matrix factorization. In Advances in Neural Information
Processing Systems, pages 3284–3292, 2014.
R. Rockafellar. Convex Analysis. Princeton Univ. Press, 1970.
16 / 17
17. Atomic norms for leveraging structure
Rockafellar [1970], Chandrasekaran et al. [2012]
Let A be a collection of atoms
x =
a∈A
caa
Atomic norm on A:
γA(x) := inf
c
{
a∈A
ca | ca ≥ 0,
a∈A
caa = x}
Example of trace norm
Matrix M ∈ Rn×p of rank k.
SVD: M = k
i=1 ci ui vi
M tr :=
k
i=1
|ci | = γA(M)
A := set of rank one matrices uv with u 2
2 ≤ 1, v 2
2 ≤ 1 17 / 17