Sunday, August 26, 2018
Thursday, August 23, 2018
Wednesday, August 22, 2018
Ml crash directory
Are you familiar with regression (0-5.59)? One way to view Ml is regression on steroids...which mean a harder optimization problem (one that does not have a close analytic solution and/or is not convex) with many parameters.
Let's consider supervised learning first. You are given n labeled data points,
( x1,y1),...,(xn,yn). Your objective is to find a function f(x)=y that best predicts y on a new batch of x's. When y is continuous it is called regression and when its discrete it is called classification.
There are two things to notice right away
1. To solve this an optimization problem is defined, e.g., a minimization of square error in our original regression problem
2. Trying to explain the given data completely which is sometimes called extrapolation is actually a pitfall. You may capture random trends and your prediction power may be hindered. This is called overfitting
The basic intuition underlying many approaches to the classification problem is that had we known p(x, y) and given a new x we would have calculated p(x, y) for each y and choose y with the greatest probability. The difficulty is that it is not easy to estimate p(x, y).
View reference two below up to 8.15.
To estimate p(x y) we could proceed as follows. Recall that p(x y) = p(x |y)p(y) = p(y|x)p(x). Thus, estimating p(x), p(y) and p(x|y) from the training data will let us estimate p(x y) and p(y|x) and thus decide given a new x its class y. A simplifying independence assumption leads to the naive Bayes approach that is intuitively covered in the first part of Ariel Kleiner's crash course on ML (up to slide 25). This is an instance of what is referred to as generative models.
Yet another approach is to define an optimization that attempts to maximize performance on the training data while keeping f(x) simple. This is done in a varieties of ways.
To deep dive on ML concepts see reference three below. Iterate between reference three and simple ML tutorial in python or R to master the subject.
References
1. Introduction to programmers on why ml is useful to master. Notice that this introduction
ignores the challenges of applying it where it excels and dealing with drift.
2. Nice overview that start with classification only thing to be careful of is the claim that neural network are not statistical models. Estimating a neural network performance should be done using the same standard statistical tools, e.g., cross validation.
3. An intuitive deep dive on the concepts of machine learning is given by Haul Daume III
Are you familiar with regression (0-5.59)? One way to view Ml is regression on steroids...which mean a harder optimization problem (one that does not have a close analytic solution and/or is not convex) with many parameters.
Let's consider supervised learning first. You are given n labeled data points,
( x1,y1),...,(xn,yn). Your objective is to find a function f(x)=y that best predicts y on a new batch of x's. When y is continuous it is called regression and when its discrete it is called classification.
There are two things to notice right away
1. To solve this an optimization problem is defined, e.g., a minimization of square error in our original regression problem
2. Trying to explain the given data completely which is sometimes called extrapolation is actually a pitfall. You may capture random trends and your prediction power may be hindered. This is called overfitting
The basic intuition underlying many approaches to the classification problem is that had we known p(x, y) and given a new x we would have calculated p(x, y) for each y and choose y with the greatest probability. The difficulty is that it is not easy to estimate p(x, y).
View reference two below up to 8.15.
To estimate p(x y) we could proceed as follows. Recall that p(x y) = p(x |y)p(y) = p(y|x)p(x). Thus, estimating p(x), p(y) and p(x|y) from the training data will let us estimate p(x y) and p(y|x) and thus decide given a new x its class y. A simplifying independence assumption leads to the naive Bayes approach that is intuitively covered in the first part of Ariel Kleiner's crash course on ML (up to slide 25). This is an instance of what is referred to as generative models.
Yet another approach is to define an optimization that attempts to maximize performance on the training data while keeping f(x) simple. This is done in a varieties of ways.
To deep dive on ML concepts see reference three below. Iterate between reference three and simple ML tutorial in python or R to master the subject.
References
1. Introduction to programmers on why ml is useful to master. Notice that this introduction
ignores the challenges of applying it where it excels and dealing with drift.
2. Nice overview that start with classification only thing to be careful of is the claim that neural network are not statistical models. Estimating a neural network performance should be done using the same standard statistical tools, e.g., cross validation.
3. An intuitive deep dive on the concepts of machine learning is given by Haul Daume III
Sunday, August 19, 2018
Back to Bayesian inference - https://drive.google.com/file/d/1NUioDotuKeA8kKg341qRjyUESnUjxkos/view?usp=sharing
Monday, August 13, 2018
Ml crash directory
Are you familiar with regression - https://m.youtube.com/watch?v=aq8VU5KLmkY (0-5.59)? One way to view Ml is regression on steroids...which mean a harder optimization problem (one that does not have a close analytic solution and/or is not convex) with many parameters.
Let's consider supervised learning first. You are given n labeled data points,
( x1,y1),...,(xn,yn). Your objective is to find a function f(x)=y that best predicts y on a new batch of x's. When y is continuous it is called regression and when its discrete it is called classification.
There are two things to notice right away
1. To solve this an optimization problem is defined, e.g., a minimization of square error in our original regression problem
2. Trying to explain the given data completely which is sometimes called extrapolation is actually a pitfall. You may capture random trends and your prediction power may be hindered. This is called overfitting
The basic intuition underlying many approaches to the classification problem is that had we known p(x, y) and given a new x we would have calculated p(x, y) for each y and choose y with the greatest probability. The difficulty is that it is not easy to estimate p(x, y).
View reference two below up to 8.15.
To estimate p(x y) we could proceed as follows. Recall that p(x y) = p(x |y)p(y) = p(y|x)p(x). Thus, estimating p(x), p(y) and p(x|y) from the training data will let us estimate p(x y) and p(y|x) and thus decide given a new x its class y. A simplifying independence assumption leads to the naive Bayes approach that is intuitively covered in the first part of Ariel Kleiner's crash course on ML at http://ampcamp.berkeley.edu/wp-content/uploads/2012/06/ariel-kleiner-ampcamp-2012-machine-learning-part-1.pdf. (up to slide 25). This is an instance of what is referred to as generative models.
Yet another approach is to define an optimization that attempts to maximize performance on the training data while keeping f(x) simple. This is done in a varieties of ways.
To deep dive on ML concepts see reference three below. Iterate between reference three and simple ML tutorial in python or R to master the subject.
References
1. Introduction to programmers on why ml is useful to master -
https://m.youtube.com/watch?v=0mK52UsOj-U
Ignores the challenges of applying it where it excels and dealing with drift.
2. Nice overview that start with classification https://m.youtube.com/watch?v=z-EtmaFJieY only thing to be careful of is the claim that neural network are not statistical models. Estimating a neural network performance should be done using the same standard statistical tools, e.g., cross validation.
3. An intuitive deep dive on the concepts of machine learning is given by Haul Daume III at http://ciml.info/dl/v0_8/ciml-v0_8-all.pdf
Are you familiar with regression - https://m.youtube.com/watch?v=aq8VU5KLmkY (0-5.59)? One way to view Ml is regression on steroids...which mean a harder optimization problem (one that does not have a close analytic solution and/or is not convex) with many parameters.
Let's consider supervised learning first. You are given n labeled data points,
( x1,y1),...,(xn,yn). Your objective is to find a function f(x)=y that best predicts y on a new batch of x's. When y is continuous it is called regression and when its discrete it is called classification.
There are two things to notice right away
1. To solve this an optimization problem is defined, e.g., a minimization of square error in our original regression problem
2. Trying to explain the given data completely which is sometimes called extrapolation is actually a pitfall. You may capture random trends and your prediction power may be hindered. This is called overfitting
The basic intuition underlying many approaches to the classification problem is that had we known p(x, y) and given a new x we would have calculated p(x, y) for each y and choose y with the greatest probability. The difficulty is that it is not easy to estimate p(x, y).
View reference two below up to 8.15.
To estimate p(x y) we could proceed as follows. Recall that p(x y) = p(x |y)p(y) = p(y|x)p(x). Thus, estimating p(x), p(y) and p(x|y) from the training data will let us estimate p(x y) and p(y|x) and thus decide given a new x its class y. A simplifying independence assumption leads to the naive Bayes approach that is intuitively covered in the first part of Ariel Kleiner's crash course on ML at http://ampcamp.berkeley.edu/wp-content/uploads/2012/06/ariel-kleiner-ampcamp-2012-machine-learning-part-1.pdf. (up to slide 25). This is an instance of what is referred to as generative models.
Yet another approach is to define an optimization that attempts to maximize performance on the training data while keeping f(x) simple. This is done in a varieties of ways.
To deep dive on ML concepts see reference three below. Iterate between reference three and simple ML tutorial in python or R to master the subject.
References
1. Introduction to programmers on why ml is useful to master -
https://m.youtube.com/watch?v=0mK52UsOj-U
Ignores the challenges of applying it where it excels and dealing with drift.
2. Nice overview that start with classification https://m.youtube.com/watch?v=z-EtmaFJieY only thing to be careful of is the claim that neural network are not statistical models. Estimating a neural network performance should be done using the same standard statistical tools, e.g., cross validation.
3. An intuitive deep dive on the concepts of machine learning is given by Haul Daume III at http://ciml.info/dl/v0_8/ciml-v0_8-all.pdf
Sunday, July 29, 2018
We'll discuss latent variables and the intuition of the EM algorithm https://drive.google.com/open?id=1PcESzNbZzzMej1nA0o5CHRzzGKTw2IAd
Sunday, July 22, 2018
We'll cover LDA in tw's meeting. Here is the slide - https://drive.google.com/open?id=1KRoCA4vo9H9oJOl3iD-qRqIHl9qQq9vf
This is part of our deep dive into generative models which will eventually loops us back to BN but will also shade light on GAN approaches. Here is some background and relevant resources -
This is part of our deep dive into generative models which will eventually loops us back to BN but will also shade light on GAN approaches. Here is some background and relevant resources -
Generative models
Under the generative model approach we attempt to model the joint
distribution p(x y). Given x and applying the Bayesian rule to our model we
classify as y the y for which p(y | x) is largest.
A straight forward application of the Bayes rule is to attempt the
estimation of probabilities in the Bayesian rule p(y | x) p(x) = p(x | y) p(y).
With the typical large number of dimensions of the vector x, density
estimation of the required quantiles is really hard. See the first 30 mins
of https://m.youtube.com/watch?v=_m7TMkzZzus#fauxfullscreen for
details.
As modeling the joint distribution p(x y) is hard simplifying assumption
are introduced leading to different more concrete classification
techniques.
LDA
LDA models each p(x | y) as a gaussian distribution. This stat quest
video describes how the average and standard deviation of the distribution are
chosen to maximize the separation between the classes over the training set https://m.youtube.com/watch?v=azXCzI57Yfc
The second 30 mins of this lecture derives LDA and explains what happens if
the covariance of all class matrices are I https://m.youtube.com/watch?v=_m7TMkzZzus#
Here the estimation of a covariance matrices of a random vector is
explained in detailhttps://en.m.wikipedia.org/wiki/Estimation_of_covariance_matrices
See chapter 24 of the understanding book for a broader coverage of
generation methods - https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/understanding-machine-learning-theory-algorithms.pdf
The background required for the Gaussian distribution and the covariance
matrix is covered herehttp://cs229.stanford.edu/section/gaussians.pdf
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