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think of each of these regions as a category or symbol : by having a separate degree of freedom for each symbol ( or region ), we can learn an arbitrary decoder mapping from symbol to value. however, this does not allow us to generalize to new symbols for new regions. if we are lucky, there may be some regularity in th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 565 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
by an arrangement of n hyperplanes in rd? by applying a general result concerning the intersection of hyperplanes (, ), one can show ( zaslavsky 1975 pascanu 2014b et al., ) that the number of regions this binary feature representation can distinguish is d j = 0 n j = ( o nd ). ( 15. 4 ) therefore, we see a growth that... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 565 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning this provides a geometric argument to explain the generalization power of distributed representation : with o ( nd ) parameters ( for n linear - threshold features in rd ) we can distinctly represent o ( nd ) regions in input space. if instead we made no assumption at all about the d... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 566 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a non - distributed setting where we would need o ( r ) examples to obtain the same features and associated partitioning of the input space into r regions. using fewer parameters to represent the model means that we have fewer parameters to fit, and thus require far fewer training examples to generalize well. a further ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 566 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
that the classes to be recognized are linearly separable as a function of the underlying causal factors captured by h. we will typically want to learn categories such as the set of all images of all green objects or the set of all images of cars, but not categories that require nonlinear, xor logic. for example, we typ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 566 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning - + = figure 15. 9 : a generative model has learned a distributed representation that disentangles the concept of gender from the concept of wearing glasses. if we begin with the repre - sentation of the concept of a man with glasses, then subtract the vector representing the concept... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 567 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
one direction in representation space corresponds 15. 9 to whether the person is male or female, while another corresponds to whether the person is wearing glasses. these features were discovered automatically, not fixed a priori. there is no need to have labels for the hidden unit classifiers : gradient descent on an ob... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 567 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning 15. 5 exponential gains from depth we have seen in section that multilayer perceptrons are universal approxima - 6. 4. 1 tors, and that some functions can be represented by exponentially smaller deep networks compared to shallow networks. this decrease in model size leads to improved... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 568 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
inputs are more likely to be very high - level and related in highly nonlinear ways to the input. we argue that this demands deep distributed representations, where the higher level features ( seen as functions of the input ) or factors ( seen as generative causes ) are obtained through the composition of many nonlinea... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 568 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
expressive power of deep architectures state that there are families of functions that can be represented [UNK] by an architecture of depth k, but would require an exponential number of hidden units ( with respect to the input size ) with [UNK] depth ( depth 2 or depth ). k −1 in section, we saw that deterministic feed... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 568 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning in section, we saw that a [UNK] deep feedforward network can have 6. 4. 1 an exponential advantage over a network that is too shallow. such results can also be obtained for other models such as probabilistic models. one such probabilistic model is the sum - product network or spn ( p... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 569 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##tional nets, highlighting an exponential advantage for the deep circuit even when the shallow circuit is allowed to only approximate the function computed by the deep circuit (, cohen et al. 2015 ). by comparison, previous theoretical work made claims regarding only the case where the shallow circuit must exactly rep... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 569 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
factors of variation directly. more generally, to make use of abundant unlabeled data, representation learning makes use of other, less direct, hints about the underlying factors. these hints take the form of implicit prior beliefs that we, the designers of the learning algorithm, impose in order to guide the learner. ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 569 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning we provide here a list of these generic regularization strategies. the list is clearly not exhaustive, but gives some concrete examples of ways that learning algorithms can be encouraged to discover features that correspond to underlying factors. this list was introduced in section 3... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 570 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
functions with large weights applied to high - dimensional spaces may not be very smooth. see goodfellow et al. ( ) for a further discussion of the limitations of the linearity assumption. 2014b • multiple explanatory factors : many representation learning algorithms are motivated by the assumption that the data is gen... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 570 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
observed data x, and not vice - versa. as discussed in section, this 15. 3 is advantageous for semi - supervised learning and makes the learned model more robust when the distribution over the underlying causes changes or when we use the model for a new task. • depth a hierarchical organization of explanatory factors, ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 570 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning expresses our belief that the task should be accomplished via a multi - step program, with each step referring back to the output of the processing accomplished via previous steps. • shared factors across tasks : in the context where we have many tasks, corresponding to [UNK] yi vari... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 571 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
algorithms behave sensibly only on this manifold (, ). some machine learning algorithms, especially goodfellow et al. 2014b autoencoders, attempt to explicitly learn the structure of the manifold. • natural clustering : many machine learning algorithms assume that each connected manifold in the input space may be assig... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 571 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
describing most inputs — there is no need to use a feature that detects elephant trunks when representing an image of a cat. it is therefore reasonable to impose a prior that any feature that can be interpreted as “ present ” or “ absent ” should be absent most of the time. • simplicity of factor dependencies : in good... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 571 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 15. representation learning possible is marginal independence, p ( h ) = ip ( hi ), but linear dependencies or those captured by a shallow autoencoder are also reasonable assumptions. this can be seen in many laws of physics, and is assumed when plugging a linear predictor or a factorized prior on top of a lear... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 572 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16 structured probabilistic models for deep learning deep learning draws upon many modeling formalisms that researchers can use to guide their design [UNK] and describe their algorithms. one of these formalisms is the idea of structured probabilistic models. we have already discussed structured probabilistic mo... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 573 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
each other directly. here we use “ graph ” in the graph theory sense — a set of vertices connected to one another by a set of edges. because the structure of the model is defined by a graph, these models are often also referred to as graphical models. the graphical models research community is large and has developed ma... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 573 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning may benefit from reading the final section of this chapter, section, in which we 16. 7 highlight some of the unique ways that graphical models are used for deep learning algorithms. deep learning practitioners tend to use very [UNK] model structures, learning ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 574 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
cies in section. finally, we close with a discussion of the unique emphasis that 16. 5 deep learning practitioners place on specific approaches to graphical modeling in section. 16. 7 16. 1 the challenge of unstructured modeling the goal of deep learning is to scale machine learning to the kinds of challenges needed to ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 574 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
classifier is also often able to ignore many parts of the input. for example, when recognizing an object in a photo, it is usually possible to ignore the background of the photo. it is possible to ask probabilistic models to do many other tasks. these tasks are often more expensive than classification. some of them requi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 574 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning the input, with no option to ignore sections of it. these tasks include the following : • density estimation : given an input x, the machine learning system returns an estimate of the true density p ( x ) under the data generating distribution. this requires... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 575 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to return estimates of or a probability distribution over some or all of the unobserved elements of x. this requires multiple outputs. because the model could be asked to restore any of the elements of x, it must understand the entire input. • sampling : the model generates new samples from the distribution p ( x ). ap... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 575 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
images of this form. this number is over 10800 times larger than the estimated number of atoms in the universe. in general, if we wish to model a distribution over a random vector x containing n discrete variables capable of taking on k values each, then the naive approach of representing p ( x ) by storing a lookup ta... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 575 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning figure 16. 1 : probabilistic modeling of natural images. ( top ) example 32× 32 pixel color images from the cifar - 10 dataset (, ). samples krizhevsky and hinton 2009 ( bottom ) drawn from a structured probabilistic model trained on this dataset. each sampl... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 576 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning • memory : the cost of storing the representation : for all but very small values of n and k, representing the distribution as a table will require too many values to store. • statistical [UNK] : as the number of parameters in a model increases, so does the ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 577 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
distribution p ( x2 | x1 ). computing these distributions will require summing across the entire table, so the runtime of these operations is as high as the intractable memory cost of storing the model. • runtime : the cost of sampling : likewise, suppose we want to draw a sample from the model. the naive way to do thi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 577 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. suppose the team consists of three runners : alice, bob and carol. at the start of the race, alice carries a baton and begins running around a track. after completing her lap around the track, she hands the baton to bob. bob then runs his own lap and hands the baton to carol, who runs the final lap. we can model each ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 577 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning equal. finally, carol ’ s finishing time depends on both her teammates. if alice is slow, bob will probably finish late too. as a consequence, carol will have quite a late starting time and thus is likely to have a late finishing time as well. however, carol ’ ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 578 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ficantly fewer parameters and therefore be estimated reliably from less data. these smaller models also have dramatically reduced computational cost in terms of storing the model, performing inference in the model, and drawing samples from the model. 16. 2 using graphs to describe model structure structured probabilis... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 578 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
known as the belief network bayesian network or 2 ( pearl 1985, ). directed graphical models are called “ directed ” because their edges are directed, 2 judea pearl suggested using the term “ bayesian network ” when one wishes to “ emphasize the judgmental ” nature of the values computed by the network, i. e. to highli... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 578 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning t0t0 t1t1 t2t2 alice bob carol figure 16. 2 : a directed graphical model depicting the relay race example. alice ’ s finishing time t0 influences bob ’ s finishing time t1, because bob does not get to start running until alice finishes. likewise, carol only gets... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 579 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, the distribution over b depends on the value of a. continuing with the relay race example from section, suppose we name 16. 1 alice ’ s finishing time t0, bob ’ s finishing time t1, and carol ’ s finishing time t2. as we saw earlier, our estimate of t1 depends on t0. our estimate of t2 depends directly on t1 but only in... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 579 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
) in our relay race example, this means that, using the graph drawn in figure, 16. 2 p ( t0, t1, t2 ) = ( p t0 ) ( p t 1 | t0 ) ( p t2 | t1 ). ( 16. 2 ) this is our first time seeing a structured probabilistic model in action. we can examine the cost of using it, in order to observe how structured modeling has many advan... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 579 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning redundant by the constraint that the sum of the probabilities be 1 ). if instead, we only make a table for each of the conditional probability distributions, then the distribution over t0 requires 99 values, the table defining t1 given t0 requires 9900 values... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 580 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
as we can design a model such that m < < n, we get very dramatic savings. in other words, so long as each variable has few parents in the graph, the distribution can be represented with very few parameters. some restrictions on the graph structure, such as requiring it to be a tree, can also guarantee that operations l... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 580 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
and lazy ). then the only [UNK] alice has on bob ’ s finishing time is that we must add alice ’ s finishing time to the total amount of time we think bob needs to run. this observation allows us to define a model with o ( k ) parameters instead of o ( k2 ). however, note that t0 and t1 are still directly dependent with th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 580 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning our conditional distributions. it only defines which variables they are allowed to take in as arguments. 16. 2. 2 undirected models directed graphical models give us one language for describing structured probabilis - tic models. another popular language is t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 581 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to their interactions. when the interactions seem to have no intrinsic direction, or to operate in both directions, it may be more appropriate to use an undirected model. as an example of such a situation, suppose we want to model a distribution over three binary variables : whether or not you are sick, whether or not ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 581 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
from your coworker to you and the transmission of the cold from you to your roommate. in this case, it is just as easy for you to cause your roommate to get sick as it is for your roommate to make you sick, so there is not a clean, uni - directional narrative on which to base the model. this motivates using an undirect... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 581 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning hrhr hyhy hchc figure 16. 3 : an undirected graph representing how your roommate ’ s healthhr, your health hy, and your work colleague ’ s health hc [UNK] each other. you and your roommate might infect each other with a cold, and you and your work colleague ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 582 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ique potential ) measures the [UNK] of the variables in that clique for being in each of their possible joint states. the factors are constrained to be non - negative. together they define an unnormalized probability distribution [UNK] ( ) = π x c∈g φ. ( ) c ( 16. 3 ) the unnormalized probability distribution is [UNK]... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 582 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a table, and might have values resembling these : hy = 0 hy = 1 hc = 0 2 1 hc = 1 1 10 3a clique of the graph is a subset of nodes that are all connected to each other by an edge of the graph. 567 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 582 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a state of 1 indicates good health, while a state of 0 indicates poor health ( having been infected with a cold ). both of you are usually healthy, so the corresponding state has the highest [UNK]. the state where only one of you is sick has the lowest [UNK]... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 583 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
) where z is the value that results in the probability distribution summing or integrating to 1 : z = [UNK] d. ( ) x x ( 16. 5 ) you can think of z as a constant when the φ functions are held constant. note that if the φ functions have parameters, then z is a function of those parameters. it is common in the literature... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 583 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
topic of chapter. 18 one important consideration to keep in mind when designing undirected models is that it is possible to specify the factors in such a way that z does not exist. this happens if some of the variables in the model are continuous and the integral 4a distribution defined by normalizing a product of cliqu... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 583 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning of [UNK] over their domain diverges. for example, suppose we want to model a single scalar variable x with a single clique potential ∈r φ x x ( ) = 2. in this case, z = x2dx. ( 16. 6 ) since this integral diverges, there is no probability distribution corres... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 584 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
distributions. this changes the intuitions one must develop in order to work with these models. one key idea to keep in mind while working with undirected models is that the domain of each of the variables has dramatic [UNK] on the kind of probability distribution that a given set of φ functions corresponds to. for exa... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 584 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
( bi ). if the domain of x is the set of elementary basis vectors ( { [ 1, 0,..., 0 ], [ 0, 1,..., 0 ],..., [ 0, 0,..., 1 ] } ) then p ( x ) = softmax ( b ), so a large value of bi actually reduces p ( xj = 1 ) for j = i. often, it is possible to leverage the [UNK] of a carefully chosen domain of a variable in order to... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 584 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a b c d e f figure 16. 4 : this graph implies that p ( a b c d e f,,,,, ) can be written as 1 z φa b, ( a b, ) φb c, ( b c, ) φa d, ( a d, ) φb e, ( b e, ) φe f, ( e f, ) for an appropriate choice of the φ func - tions. and e ( x ) is known as the energy fun... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 585 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
5 the probabilities in an energy - based model can approach arbitrarily close to zero but never reach it. any distribution of the form given by equation is an example of a 16. 7 boltz - mann distribution. for this reason, many energy - based models are called boltzmann machines ( fahlman 1983 ackley 1985 hinton et al.,... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 585 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
with latent variables, while boltzmann machines without latent variables are more often called markov random fields or log - linear models. cliques in an undirected graph correspond to factors of the unnormalized probability function. because exp ( a ) exp ( b ) = exp ( a + b ), this means that [UNK] cliques in the undi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 585 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a b c d e f figure 16. 5 : this graph implies that e ( a b c d e f,,,,, ) can be written as ea b, ( a b, ) + eb c, ( b c, ) + ea d, ( a d, ) + eb e, ( b e, ) + ee f, ( e f, ) for an appropriate choice of the per - clique energy functions. note that we can ob... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 586 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
corresponds to another factor in the probability distribution. each term of the energy function can be thought of as an “ expert ” that determines whether a particular soft constraint is satisfied. each expert may enforce only one constraint that concerns only a low - dimensional projection of the random variables, but ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 586 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
as “ energy ” and “ partition function ” remains associated with these techniques, even though their mathematical applicability is broader than the physics context in which they were developed. some machine learning researchers ( e. g., ( ), who smolensky 1986 referred to negative energy as harmony ) have chosen to emi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 586 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a s b a s b ( a ) ( b ) figure 16. 6 : ( a ) the path between random variablea and random variable b through s is active, because s is not observed. this means that a and b are not separated. ( b ) here s is shaded in, to indicate that it is observed. becaus... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 587 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, we would like to know which subsets of variables are conditionally independent from each other, given the values of other subsets of variables. identifying the conditional independences in a graph is very simple in the case of undirected models. in this case, conditional independence implied by the graph is called se... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 587 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. 6 model look when drawn in this way. see figure for an example of reading 16. 7 separation from an undirected graph. similar concepts apply to directed models, except that in the context of directed models, these concepts are referred to as d - separation. the “ d ” stands for “ dependence. ” d - separation for direct... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 587 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a b c d figure 16. 7 : an example of reading separation properties from an undirected graph. here b is shaded to indicate that it is observed. because observingb blocks the only path from a to c, we say that a and c are separated from each other given b. the... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 588 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
directed nets, determining whether a path is active is somewhat more complicated. see figure for a guide to identifying active paths in a 16. 8 directed model. see figure for an example of reading some properties from a 16. 9 graph. it is important to remember that separation and d - separation tell us only about those c... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 588 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. encoding the behavior when a = 1 requires an edge connecting b and c. the graph then fails to indicate that b and c are independent when a. = 0 in general, a graph will never imply that an independence exists when it does not. however, a graph may fail to encode an independence. 573 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 588 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a s b a s b a s b a s b a s b c ( a ) ( b ) ( c ) ( d ) figure 16. 8 : all of the kinds of active paths of length two that can exist between random variables a and b. any path with arrows proceeding directly from ( a ) a to b or vice versa. this kind of path... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 589 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
what is observed at a. a lower than expected wind at a ( for a hurricane ) would not change our expectation of winds atb ( knowing there is a hurricane ). however, if s is not observed, then a and b are dependent, i. e., the path is active. ( c ) a and b are both parents of s. this is called a v - structure or the coll... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 589 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
you can infer that she is probably not also explain sick. the explaining away [UNK] happens even if any descendant of ( d ) s is observed! for example, suppose that c is a variable representing whether you have received a report from your colleague. if you notice that you have not received the report, this increases yo... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 589 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a b c d e figure 16. 9 : from this graph, we can read out several d - separation properties. examples include : • a and b are d - separated given the empty set. • a and e are d - separated given c. • d and e are d - separated given c. we can also see that so... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 590 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning 16. 2. 6 converting between undirected and directed graphs we often refer to a specific machine learning model as being undirected or directed. for example, we typically refer to rbms as undirected and sparse coding as directed. this choice of wording can be ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 591 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
distribution. there are other factors that can [UNK] the decision of which language to use. even while working with a single probability distribution, we may sometimes switch between [UNK] modeling languages. sometimes a [UNK] language becomes more appropriate if we observe a certain subset of variables, or if we wish ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 591 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
precede it in the ordering as its ancestors in the graph. for an undirected model, the complete graph is simply a graph containing a single clique encompassing all of the variables. see figure for an example. 16. 10 of course, the utility of a graphical model is that the graph implies that some variables do not interact... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 591 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning figure 16. 10 : examples of complete graphs, which can describe any probability distribution. here we show examples with four random variables. ( left ) the complete undirected graph. in the undirected case, the complete graph is unique. a complete directed ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 592 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
represent perfectly. this substructure is called an immorality. the structure occurs when two random variables a and b are both parents of a third random variable c, and there is no edge directly connecting a and b in either direction. ( the name “ immorality ” may seem strange ; it was coined in the graphical models l... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 592 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
can represent perfectly. specifically, a directed graph cannot capture all of the d conditional independences implied by an undirected graph u if u contains a loop of length greater than three, unless that loop also contains a chord. a loop is a sequence of variables connected by undirected edges, with the last variable... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 592 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning h1h1 h2h2 h3h3 v1 v1 v2 v2 v3 v3 a b c a c b h1h1 h2h2 h3h3 v1 v1 v2 v2 v3 v3 a b c a c b figure 16. 11 : examples of converting directed models ( top row ) to undirected models ( bottom row ) by constructing moralized graphs. ( left ) this simple chain can ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 593 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
this dependence, the undirected model must include a clique encompassing all three variables. this clique fails to encode the fact thata b [UNK]. ( right ) in general, moralization may add many edges to the graph, thus losing many implied independences. for example, this sparse coding graph requires adding moralizing e... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 593 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning a b d c a b d c a b d c figure 16. 12 : converting an undirected model to a directed model. ( left ) this undirected model cannot be converted directed to a directed model because it has a loop of length four with no chords. specifically, the undirected model... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 594 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
each edge. when doing so, we must not create any directed cycles. one way to avoid directed cycles is to impose an ordering over the nodes, and always point each edge from the node that comes earlier in the ordering to the node that comes later in the ordering. in this example, we use the variable names to impose alpha... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 594 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to the node that comes later in the ordering. see figure for a demonstration. 16. 12 16. 2. 7 factor graphs factor graphs are another way of drawing undirected models that resolve an ambiguity in the graphical representation of standard undirected model syntax. in an undirected model, the scope of every φ function must ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 594 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning factor graphs resolve this ambiguity by explicitly representing the scope of each φ function. specifically, a factor graph is a graphical representation of an undirected model that consists of a bipartite undirected graph. some of the nodes are drawn as circl... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 595 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
c f1f1 a b c f1f1 f2f2 f3f3 figure 16. 13 : an example of how a factor graph can resolve ambiguity in the interpretation of undirected networks. ( left ) an undirected network with a clique involving three variables : a, b and c. a factor graph corresponding to the same undirected model. this ( center ) factor graph ha... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 595 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning can then be sampled in this order. in other words, we first sample x1 [UNK] ( x1 ), then sample p ( x2 | pag ( x2 ) ), and so on, until finally we sample p ( xn | pag ( xn ) ). so long as each conditional distribution p ( xi | pag ( xi ) ) is easy to sample fr... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 596 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
directed graphical models. another drawback is that it does not support every conditional sampling operation. when we wish to sample from a subset of the variables in a directed graphical model, given some other variables, we often require that all the condition - ing variables come earlier than the variables to be sam... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 596 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the resulting directed model becomes intractable. sampling from an undirected model without first converting it to a directed model seems to require resolving cyclical dependencies. every variable interacts with every other variable, so there is no clear beginning point for the sampling process. unfortunately, drawing s... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 596 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning process and resample all n variables using the updated values of their neighbors. asymptotically, after many repetitions, this process converges to sampling from the correct distribution. it can be [UNK] to determine when the samples have reached a [UNK] acc... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 597 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
model a direct interaction. a less quantifiable benefit of using structured probabilistic models is that they allow us to explicitly separate representation of knowledge from learning of knowledge or inference given existing knowledge. this makes our models easier to develop and debug. we can design, analyze, and evaluat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 597 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the model can then capture dependencies between any pair of variables vi and vj indirectly, via direct dependencies between vi and h, and direct dependencies between and v h j. a good model of v which did not contain any latent variables would need to 582 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 597 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning have very large numbers of parents per node in a bayesian network or very large cliques in a markov network. just representing these higher order interactions is costly — both in a computational sense, because the number of parameters that must be stored in ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 598 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a score. the score rewards high training set accuracy and penalizes model complexity. candidate structures with a small number of edges added or removed are then proposed as the next step of the search. the search proceeds to a new structure that is expected to increase the score. using latent variables instead of adap... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 598 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
of gaussians model can be used to do classification. in chapter we saw how simple probabilistic models like sparse 14 coding learn latent variables that can be used as input features for a classifier, or as coordinates along a manifold. other models can be used in this same way, but deeper models and models with [UNK] ki... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 598 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning 16. 6 inference and approximate inference one of the main ways we can use a probabilistic model is to ask questions about how variables are related to each other. given a set of medical tests, we can ask what disease a patient might have. in a latent variabl... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 599 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. unfortunately, for most interesting deep models, these inference problems are intractable, even when we use a structured graphical model to simplify them. the graph structure allows us to represent complicated, high - dimensional distributions with a reasonable number of parameters, but the graphs used for deep learn... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 599 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
of the clauses are satisfied. this can be done without making a large clique, by building a reduction tree of latent variables, with each node in the tree reporting whether two other variables are satisfied. the leaves of this tree are the variables for each clause. the root of the tree reports whether the entire problem... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 599 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning true distribution p ( h | v ) by seeking an approximate distribution q ( h v | ) that is as close to the true one as possible. this and other techniques are described in depth in chapter. 19 16. 7 the deep learning approach to structured prob - abilistic mod... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 600 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
we usually describe the depth of the model as being the greatest depth of any such hi. this kind of depth is [UNK] from the depth induced by the computational graph. many generative models used for deep learning have no latent variables or only one layer of latent variables, but use deep computational graphs to define t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 600 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
nonlinear interactions between variables. if there are latent variables, they are usually few in number. the way that latent variables are designed also [UNK] in deep learning. the deep learning practitioner typically does not intend for the latent variables to take on any specific semantics ahead of time — the training... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 600 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 16. structured probabilistic models for deep learning usually not very easy for a human to interpret after the fact, though visualization techniques may allow some rough characterization of what they represent. when latent variables are used in the context of traditional graphical models, they are often designe... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 601 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
model structure is tightly linked with the choice of inference algorithm. traditional approaches to graphical models typically aim to maintain the tractability of exact inference. when this constraint is too limiting, a popular approximate inference algorithm is an algorithm called loopy belief propagation. both of the... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 601 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. another consideration is that deep learning models contain a very large number of latent variables, making [UNK] numerical code essential. this provides an additional motivation, besides the choice of high - level inference algorithm, for grouping the units into layers with a matrix describing the interaction between... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 601 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
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