The document discusses various techniques for smoothing N-gram language models, including Laplace smoothing, Good-Turing discounting, and backoff models. Laplace smoothing involves adding one to all counts to address unseen events. Good-Turing smoothing estimates probabilities for low counts based on the frequency of higher counts. Backoff models first use the highest available order N-gram model and only fallback to a lower order if the current count is zero.
This lecture is all about General problem Solver, a universal Problem Solving Machine using Same Base Algorithm.
and is for BS computer Science Students.
it is only for learning purpose, is not that much professional, there may be errors or mistakes, therefore corrections and suggestions are welcome.
This is the presentation on Syntactic Analysis in NLP.It includes topics like Introduction to parsing, Basic parsing strategies, Top-down parsing, Bottom-up
parsing, Dynamic programming – CYK parser, Issues in basic parsing methods, Earley algorithm, Parsing
using Probabilistic Context Free Grammars.
This lecture talks about parsing. Briefly gives overview on lexicon, categorization, grammar rules, syntactic tree, word senses and various challenges of natural language processing
Numerical Analysis and Its application to Boundary Value ProblemsGobinda Debnath
here is a presentation that I have presented on a webinar. in this presentation, I mainly focused on the application of numerical analysis to Boundary Value problems. I described one of the most useful traditional methods called the finite difference method. those who are interested to do research in applied mathematics, CFD, Numerical analysis may go through it for the basic ideas.
This lecture is all about General problem Solver, a universal Problem Solving Machine using Same Base Algorithm.
and is for BS computer Science Students.
it is only for learning purpose, is not that much professional, there may be errors or mistakes, therefore corrections and suggestions are welcome.
This is the presentation on Syntactic Analysis in NLP.It includes topics like Introduction to parsing, Basic parsing strategies, Top-down parsing, Bottom-up
parsing, Dynamic programming – CYK parser, Issues in basic parsing methods, Earley algorithm, Parsing
using Probabilistic Context Free Grammars.
This lecture talks about parsing. Briefly gives overview on lexicon, categorization, grammar rules, syntactic tree, word senses and various challenges of natural language processing
Numerical Analysis and Its application to Boundary Value ProblemsGobinda Debnath
here is a presentation that I have presented on a webinar. in this presentation, I mainly focused on the application of numerical analysis to Boundary Value problems. I described one of the most useful traditional methods called the finite difference method. those who are interested to do research in applied mathematics, CFD, Numerical analysis may go through it for the basic ideas.
Introduction to basic Mathematics , multiplication, division, addition and subtraction with concept of BODMAS .Basic operations fractions , decimals and percentage.
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
Lecture 5 - Gradient Descent, a lecture in subject module Statistical & Machi...Maninda Edirisooriya
Gradient Descent is the most commonly used learning algorithm for learning, including Deep Neural Networks with Back Propagation. This was one of the lectures of a full course I taught in University of Moratuwa, Sri Lanka on 2023 second half of the year.
Data Science - Part XII - Ridge Regression, LASSO, and Elastic NetsDerek Kane
This lecture provides an overview of some modern regression techniques including a discussion of the bias variance tradeoff for regression errors and the topic of shrinkage estimators. This leads into an overview of ridge regression, LASSO, and elastic nets. These topics will be discussed in detail and we will go through the calibration/diagnostics and then conclude with a practical example highlighting the techniques.
At the end of this lecture students should be able to;
Define the C standard functions for managing file input output.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Define the declaration C strings.
Compare fixed length and variable length string.
Apply strings for functions.
Define string handling functions.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Define, initialize and access to the C stuctuers.
Develop programs using structures in arrays and functions.
Use structures within structures and structures as pointers.
Define, initialize and access to the C unions.
Compare and contrast C structures and unions.
Define memory allocation and de-allocation methods in C.
Develop programs using memory allocation functions.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Define the C standard functions for managing input output.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Define the C pointers and its usage in computer programming.
Describe pointer declaration and initialization.
Apply C pointers for expressions.
Experiment on pointer operations.
Identify NULL pointer concept.
Experiment on pointer to pointer, pointer arrays, arrays with pointers and functions with pointers.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Describe the C arrays.
Practice the declaration, initialization and access linear arrays.
Practice the declaration, initialization and access two dimensional arrays.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Describe the looping structures in C programming language.
Practice the control flow of different looping structures in C programming language.
Practice the variants in control flow of different looping structures in C programming language.
Apply taught concepts for writing programs.
COM1407: Program Control Structures – Decision Making & BranchingHemantha Kulathilake
At the end of this lecture students should be able to;
Define the operation of if, if-else, nested if-else, switch and conditional operator.
Justify the control flow of the program under the aforementioned C language constructs.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Define the terms operators, operands, operator precedence and associativity.
Describe operators in C programming language.
Practice the effect of different operators in C programming language.
Justify evaluation of expressions in programming.
Apply taught concepts for writing programs.
COM1407: Type Casting, Command Line Arguments and Defining Constants Hemantha Kulathilake
At the end of this lecture students should be able to;
Define type cast and type promotion in C programming language.
Define command line arguments in C Programming language.
Declare constants according to the C programming.
Apply math.h header file for problem solving.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Define Keywords / Reserve Words in C programming language.
Define Identifiers, Variable, Data Types, Constants and statements in C Programming language.
Justify the internal process with respect to the variable declaration and initialization.
Apply Variable Declaration and Variable initialization statement.
Assigning values to variables.
Apply taught concepts for writing programs.
At the end of this lecture students should be able to;
Describe features of C programming language.
Justify the terminology related to computer programming.
Define the editing, compiling, linking, debugging stages of C programming
Recognize the basic structure of a C program
Apply comments for C programs to improve readability.
At the end of this lecture students should be able to;
Define fundamentals of data processing in computer.
Define fundamental terms in computer programming.
Define the phases of program development life cycle.
Define structured program theorem.
At the end of this lesson, you should be able to;
describe Connected Components and Contours in image segmentation.
discuss region based segmentation method.
discuss Region Growing segmentation technique.
discuss Morphological Watersheds segmentation.
discuss Model Based Segmentation.
discuss Motion Segmentation.
implement connected components, flood fill, watershed, template matching and frame difference techniques.
formulate possible mechanisms to propose segmentation methods to solve problems.
At the end of this lesson, you should be able to;
define segmentation.
Describe edge based in segmentation.
describe thresholding and its properties.
apply edge detection and thresholding as segmentation techniques.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
2. Smoothing
• What do we do with words that are in our vocabulary (they are not
unknown words) but appear in a test set in an unseen context (for
example they appear after a word they never appeared after in
training)?
• To keep a language model from assigning zero probability to these
unseen events, we’ll have to shave off a bit of probability mass from
some more frequent events and give it to the events we’ve never
seen.
• This modification is called smoothing or discounting.
• There are variety of ways to do smoothing:
– Add-1 smoothing
– Add-k smoothing
– Good-Turing Discounting
– Stupid backoff
– Kneser-Ney smoothing and many more
3. Laplace Smoothing / Add 1 Smoothing
• The simplest way to do smoothing is to add one to all
the bigram counts, before we normalize them into
probabilities.
• All the counts that used to be zero will now have a
count of 1, the counts of 1 will be 2, and so on.
• This algorithm is called Laplace smoothing.
• Laplace smoothing does not perform well enough to be
used in modern N-gram models, but it usefully
introduces many of the concepts that we see in other
smoothing algorithms, gives a useful baseline, and is
also a practical smoothing algorithm for other tasks like
text classification.
4. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• Let’s start with the application of Laplace smoothing to
unigram probabilities.
• Recall that the unsmoothed maximum likelihood estimate
of the unigram probability of the word wi is its count ci
normalized by the total number of word tokens N:
𝑃 𝑊𝑖 =
𝐶𝑖
𝑁
• Laplace smoothing merely adds one to each count.
• Since there are V words in the vocabulary and each one
was incremented, we also need to adjust the denominator
to take into account the extra V observations.
𝑃𝐿𝑎𝑝𝑙𝑎𝑐𝑒 𝑊𝑖 =
𝐶𝑖 + 1
𝑁 + 𝑉
5. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• Instead of changing both the numerator and
denominator, it is convenient to describe how a
smoothing algorithm affects the numerator, by defining
an adjusted count C*.
• This adjusted count is easier to compare directly with
the MLE counts and can be turned into a probability
like an MLE count by normalizing by N.
• To define this count, since we are only changing the
numerator in addition to adding 1 we’ll also need to
multiply by a normalization factor
𝑁
𝑁+𝑉
:
𝐶𝑖
∗
= (𝐶𝑖 + 1)
𝑁
𝑁 + 𝑉
6. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• A related way to view smoothing is as discounting
(lowering) some non-zero counts in order to get
the probability mass that will be assigned to the
zero counts.
• Thus, instead of referring to the discounted
counts c, we might describe a smoothing
algorithm in terms of a relative discount dc, the
ratio of the discounted counts to the original
counts:
𝑑 𝑐 =
𝐶∗
𝐶
9. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• Recall that normal bigram probabilities are computed by
normalizing each row of counts by the unigram count:
𝑃 𝑊𝑛 𝑊𝑛−1 =
𝐶(𝑊𝑛−1 𝑊𝑛)
𝐶(𝑊𝑛−1)
• For add-one smoothed bigram counts, we need to augment the
unigram count by the number of total word types in the vocabulary
V:
𝑃𝐿𝑎𝑝𝑙𝑎𝑐𝑒
∗
𝑊𝑛 𝑊𝑛−1 =
𝐶 𝑊𝑛−1 𝑊𝑛 + 1
𝐶 𝑊𝑛−1 + 𝑉
• Thus, each of the unigram counts given in the previous table will
need to be augmented by V =1446.
• Ex:𝑃𝐿𝑎𝑝𝑙𝑎𝑐𝑒
∗
𝑡𝑜 𝐼 =
𝐶 𝐼,𝑡𝑜 +1
𝐶 𝐼 +𝑉
=
0+1
2500+1446
=
1
3946
= 0.000253
10. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• Following table shows the add-one smoothed
probabilities for the bigrams:
11. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• It is often convenient to reconstruct the count
matrix so we can see how much a smoothing
algorithm has changed the original counts.
• These adjusted counts can be computed by
using following equation:
𝐶∗
(𝑊𝑛−1 𝑊𝑛 ) =
[𝐶 𝑊𝑛−1 𝑊𝑛 ] × 𝐶(𝑊𝑛−1)
𝐶 𝑊𝑛−1 + 𝑉
12. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• Following table shows the reconstructed
counts:
13. Laplace Smoothing / Add 1 Smoothing
(Cont…)
• Note that add-one smoothing has made a very big change to the
counts.
• C(want to) changed from 608 to 238!
• We can see this in probability space as well: P(to|want) decreases
from .66 in the unsmoothed case to .26 in the smoothed case.
• Looking at the discount d (the ratio between new and old counts)
shows us how strikingly the counts for each prefix word have been
reduced; the discount for the bigram want to is .39, while the
discount for Chinese food is .10, a factor of 10!
• The sharp change in counts and probabilities occurs because too
much probability mass is moved to all the zeros.
14. Add-K Smoothing
• One alternative to add-one smoothing is to move a bit
less of the probability mass from the seen to the
unseen events.
• Instead of adding 1 to each count, we add a fractional
count k (.5? .05? .01?).
• This algorithm is therefore called add-k smoothing.
𝑃𝐴𝑑𝑑−𝑘
∗
𝑊𝑛 𝑊𝑛−1 =
𝐶 𝑊𝑛−1 𝑊𝑛 + 𝑘
𝐶 𝑊𝑛−1 + 𝑘𝑉
• Add-k smoothing requires that we have a method for
choosing k; this can be done, for example, by
optimizing on a development set (devset).
15. Good-Turing Discounting
• The basic insight of Good-Turing smoothing is to re-estimate the amount of
probability mass to assign to N-grams with zero or low counts by looking at the
number of N-grams with higher counts.
• In other words, we examine Nc, the number of N-grams that occur c times.
• We refer to the number of N-grams that occur c times as the frequency of
frequency c.
• So applying the idea to smoothing the joint probability of bigrams, N0 is the
number of bigrams b of count 0, N1 the number of bigrams with count 1, and so
on:
𝑁𝐶 =
𝑏:𝑐 𝑏 =𝑐
1
• The Good-Turing estimate gives a smoothed count c* based on the set of Nc for all
c, as follows:
𝐶∗ = (𝐶 + 1)
𝑁𝐶 + 1
𝑁𝐶
https://www.youtube.com/watch?v=z1bq4C8hFEk
16. Backoff and Interpolation
• In the backoff model, like the deleted interpolation model,
we build an N-gram model based on an (N-1)-gram model.
• The difference is that in backoff, if we have non-zero
trigram counts, we rely solely on the trigram counts and
don’t interpolate the bigram and unigram counts at all.
• We only ‘back off’ to a lower-order N-gram if we have zero
evidence for a higher-order N-gram.