Beyond Supervised Learning in .NET framework Drawing PDF 417 in .NET framework Beyond Supervised Learning ANSI/AIM I-2/5 for Java

11. Beyond Supervised Learning Using Barcode encoder for Java Control to generate, create ANSI/AIM I-2/5 image in Java applications.Java ANSI/AIM ITF 25 for Java approach has two main cha Java USS ITF 2/5 llenges: the rst is to determine the best total ordering; the second is to nd a way to measure independence. It is dif cult to determine conditional independence when there is limited data..

PDF-417 The second method is to have a score for networks, for example, using the MAP model (page 321), which takes into account t to the data and model complexity. Given such a measure, you can search for the structure that minimizes this error..

In this section we concen Java Uniform Symbology Specification ITF trate on the second method, often called a search and score method. Assume that the data is a set E of examples, where each example has a value for each variable. The aim of the search and score method is to choose a model that maximizes P(model.

data) P(data model)P(model). The likelihood, P(data model), is the product of the probability of each example. Using the product decomposition, the product of each example given the model is the product of the probability of each variable given its parents in the model. Thus, P(data.

model)P(model). = ( P(e model))P(model) = ( Pe (Xi par(Xi , model)))P(model), model e E Xi e E where par(Xi , model) den otes the parents of Xi in the model, and Pe model ( ) denotes the probability of example e as speci ed in the model. This is maximized when its logarithm is maximized. When taking logarithms, products become sums: log P(data.

model) + log P(model). e E Xi log Pe (Xi par(Xi , model))) + log P(model). model To make this approach fea Java USS ITF 2/5 sible, assume that the prior probability of the model decomposes into components for each variable. That is, we assume probability of the model decomposes into a product of probabilities of local models for each variable. Let model(Xi ) be the local model for variable Xi .

Thus, we want to maximize the following:. e E Xi log Pe (Xi par(Xi , model))) + log P(model(Xi )) model ( ( . Xi e E Xi e E Xi e log Pmodel (Xi par(Xi , model))) + Xi e log Pmodel (Xi par(Xi , model)) + log P( model(Xi )).. log P(model(Xi )). 11.3. Reinforcement Learning We could optimize this by USS ITF 2/5 for Java optimizing each variable separately, except for the fact that the parent relation is constrained by the acyclic condition of the belief network. However, given a total ordering of the variables, we have a classi cation problem in which we want to predict the probability of each variable given the predecessors in the total ordering. To represent P(Xi .

par(Xi , model)) we could use, for example, a decision tree with probabilities of the leaves [as described in Section 7.5.1 (page 321)] or learn a squashed linear function.

Given the preceding score, we can search over total orderings of the variables to maximize this score.. 11.2.5 General Case of Belief Network Learning The general case is with unknown structure, hidden variables, and missing data; we do not even know what variables exist. Two main problems exist. The rst is the problem of missing data discussed earlier.

The second problem is computational; although there is a well-de ned search space, it is prohibitively large to try all combinations of variable ordering and hidden variables. If one only considers hidden variables that simplify the model (as seems reasonable), the search space is nite, but enormous. One can either select the best model (e.

g, the model with the highest a posteriori probability) or average over all models. Averaging over all models gives better predictions, but it is dif cult to explain to a person who may have to understand or justify the model. The problem with combining this approach with missing data seems to be much more dif cult and requires more knowledge of the domain.

. Reinforcement Learning Imagine a robot that can act in a world, receiving rewards and punishments and determining from these what it should do. This is the problem of reinforcement learning. This chapter only considers fully observable, single-agent reinforcement learning [although Section 10.

4.2 (page 441) considered a simple form of multiagent reinforcement learning]. We can formalize reinforcement learning in terms of Markov decision processes (page 399), but in which the agent, initially, only knows the set of possible states and the set of possible actions.

Thus, the dynamics, P(s . a, s), and the reward fun USS ITF 2/5 for Java ction, R(s, a, s ), are initially unknown. An agent can act in a world and, after each step, it can observe the state of the world and observe what reward it obtained. Assume the agent acts to achieve the optimal discounted reward (page 402) with a discount factor .

Example 11.7 Consider the tiny reinforcement learning problem shown in Figure 11.8 (on the next page).

There are six states the agent could be in, labeled as s0 , . . .

, s5 . The agent has four actions: UpC, Up, Left, Right. That is all the agent.

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