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Machine learning: a probabilistic perspective / Kevin P. Murphy. p. cm. — ( Adaptive computation and machine learning series). Includes Degenerate pdf. Kevin P. Murphy The probabilistic approach to machine learning is closely related to available at ppti.info~tibs/stata/ppti.info Editorial Reviews. Review. An astonishing machine learning book: intuitive, full of examples, Kevin Murphy excels at unraveling the complexities of machine learning methods while motivating the reader with a stream of illustrated . MLAPP is not freely available as a PDF (unlike BRML, closest topic-wise, ESL, or ITILA).

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Download link is on slide 4, or copy/paste: ppti.info Tags: best machine learning book, kevin p. murphy, kevin patrick. Machine learning: a probabilistic perspective / Kevin P. Murphy. –. Cambridge Some basic concepts in machine learning. 16 Degenerate pdf. Murphy's Machine Learning: A Probabilistic Perspective Errata (4th and later ppti.info · update Chap 20, a year ago As the author Kevin Murphy said (I emailed him), the 2nd edition would appear .

In general, however, xi could be a complex structured object, such as an image, a sentence, an email message, a time series, a molecular shape, a graph, etc. Another variant, known as ordinal regression, occurs where label space Y has some natural ordering, such as grades A—F. The second main type of machine learning is the descriptive or unsupervised learning approach.

This is sometimes called knowledge discovery. There is a third type of machine learning, known as reinforcement learning, which is somewhat less commonly used. This is useful for learning how to act or behave when given occasional reward or punishment signals. For example, consider how a baby learns to walk.

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Unfortunately, RL is beyond the scope of this book, although we do discuss decision theory in Section 5. See e. Supervised learning 3 a b Figure 1. Some labeled training examples of colored shapes, along with 3 unlabeled test cases. Row i represents the feature vector xi.

If the class labels are not mutually exclusive e. One way to formalize the problem is as function approximation. We use the hat symbol to denote an estimate. Our main goal is to make predictions on novel inputs, meaning ones that we have not seen before this is called generalization , since predicting the response on the training set is easy we can just look up the answer.

We have two classes of object which correspond to labels 0 and 1. The inputs are colored shapes. The input features x can be discrete, continuous or a combination of the two. In addition to the inputs, we have a vector of training labels y. In Figure 1. None of these have been seen before. Thus we are required to generalize beyond the training set.

Consequently it is not clear what the right label should be in the case of the yellow circle. Similarly, the correct label for the blue arrow is unclear.

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The reader is assumed to already have some familiarity with basic concepts in probability. If not, please consult Chapter 2 for a refresher, if necessary. We will denote the probability distribution over possible labels, given the input vector x and training set D by p y x, D. In general, this represents a vector of length C. In our notation, we make explicit that the probability is conditional on the test input x, as well as the training set D, by putting these terms on the right hand side of the conditioning bar.

We are also implicitly conditioning on the form of model that we use to make predictions. When choosing between different models, we will make this assumption explicit by writing p y x, D, M , where M denotes the model. However, if the model is clear from context, we will drop M from our notation for brevity. Another application where it is important to assess risk is when playing TV game shows, such as Jeopardy.

In this game, contestants have to solve various word puzzles and answer a variety of trivia questions, but if they answer incorrectly, they lose money. Watson uses a variety of interesting techniques Ferrucci et al. We will discuss some of the basic principles behind systems such as SmartASS later in this book. Supervised learning 5 words documents 10 20 30 40 50 60 70 80 90 Figure 1.

We only show rows, for clarity. Each row is a document represented as a bag-of-words bit vector , each column is a word.

The red lines separate the 4 classes, which are in descending order comp, rec, sci, talk these are the titles of USENET groups. We can see that there are subsets of words whose presence or absence is indicative of the class.

The data is available from http: Figure generated by newsgroupsVisualize. We have already mentioned some important applciations. We give a few more examples below. A common way to represent variable-length documents in feature-vector format is to use a bag of words representation.

This is explained in detail in Section 3. In Exercise 8.

However, when we look at the brain, we seem many levels of processing. It is believed that each level is learning features or representations at increasing levels of abstraction.

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For example, the standard model of the visual cortex Hubel and Wiesel ; Serre et al. This observation has inspired a recent trend in machine learning known as deep learning see e. Note the idea can be applied to non-vision problems as well, such as speech and language. However, we caution the reader that the topic of deep learning is currently evolving very quickly, so the material in this chapter may soon be outdated.

Acquiring enough labeled data to train such models is diffcult, despite crowd sourcing sites such as Mechanical Turk. The most natural way to perform this is to use generative models.

In this section, we discuss three different kinds of deep generative models: There have been some attempts to use computer graphics and video games to generate realistic-looking images of complex scenes, and then to use this as training data for computer vision systems. Deep learning a b c Figure Observed variables are at the bottom.

The bottom level contains the observed pixels or whatever the data is , and the remaining layers are hidden. We have assumed just 3 layers for notational simplicity. The number and size of layers is usually chosen by hand, although one can also use non-parametric Bayesian methods Adams et al.

We shall call models of this form deep directed networks or DDNs. If all the nodes are binary, and all CPDs are logistic functions, this is called a sigmoid belief net Neal Slow inference also results in slow learning.

For example, we can stack a series of RBMs on top of each other, as shown in Figure Deep generative models where we are ignoring constant offset or bias terms. The main disadvantage is that training undirected models is more difficult, because of the partition function. However, below we will see a greedy layer-wise strategy for learning deep undirected models. In particular, suppose we construct a layered model which has directed arrows, except at the top, where there is an undirected bipartite graph, as shown in Figure This model is known as a deep belief network Hinton et al.

The advantage of this peculiar architecture is that we can infer the hidden states in a fast, bottom-up fashion.

This posterior is exact, even though it is fully factorized. Now the only way to get a factored posterior is if the prior p h1 W1 is a complementary prior. This is a prior which, when multiplied by the likelihood p v h1 , results in a perfectly factored posterior.

Thus we see that the top level RBM in a DBN acts as a complementary prior for the bottom level directed sigmoidal likelihood function.

Below we show that this is a valid variational lower bound. This bound also suggests a layer-wise training strategy, that we will explain in more detail later. Note, however, that top-down inference in a DBN is not tractable, so DBNs are usually only used in a feedforward manner.

However, this terminology is non-standard. Figure 2. Used with kind permission of Ruslan Salakhutdinov. The input data to this new RBM is the activation of the hidden units E [h1 v, W1] which can be computed using a factorial approximation. One can show Hinton et al.

In practice, we want to be able to use any number of hidden units in each level. This voids the theoretical guarantee. Nevertheless the method works well in practice, as we will see. This works as follows. Perform an upwards sampling pass to the top. Finally, perform a downwards ancestral sampling pass which is an approximate sample from the posterior , and update the logistic CPD parameters using a small gradient step.

This is called the up-down procedure Hinton et al. Unfortunately this procedure is very slow. Deep neural networks The resulting training methods are often simpler to implement, and can be faster.

Note, however, that performance with deep neural nets is sometimes not as good as with probabilistic models Bengio et al.

One reason for this is that probabilistic models support top-down inference as well as bottom-up inference. Top-down inference is useful when there is a lot of ambiguity about the correct interpretation of the signal. It is interesting to note that in the mammalian visual cortex, there are many more feedback connections than there are feedforward connections see e. The role of these feedback connections is not precisely understood, but they presumably provide contextual prior information e.

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Of course, we can simulate the effect of top-down inference using a neural network. However the models we discuss below do not do this. Kevin Murphy. MIT Press, Pattern Recognition and Machine Learning. Christopher Bishop. First Edition, Springer, Pattern Classification. Second Edition, Wiley-Interscience, Machine Learning. Tom Mitchell. First Edition, McGraw-Hill, Assignment Submission Instructions You are free to discuss the assignment problems with other students in the class.

You should use one of these two languages for programming your assignments unless otherwise explicitly allowed.The study also showed that many women need at least minutes of intercourse to reach "The Big O" - and, worse still Notes on conjugate gradient descent , from Jonathan Shewchuk with good insights into geometric aspects of optimization in general Slides from Stephen Wright optimization and machine learning: IPAM slides and NIPS slides see also video.

Markov models. Jan 1, Covers far more than we will cover in this week class.

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