Markov Chains
... We illustrate Theorem 11.12 by writing a program to simulate the behavior of a Markov chain. SimulateChain is such a program. Example 11.21 In the Land of Oz, there are 525 days in a year. We have simulated the weather for one year in the Land of Oz, using the program SimulateChain. The results are ...
... We illustrate Theorem 11.12 by writing a program to simulate the behavior of a Markov chain. SimulateChain is such a program. Example 11.21 In the Land of Oz, there are 525 days in a year. We have simulated the weather for one year in the Land of Oz, using the program SimulateChain. The results are ...
Intercausal Reasoning with Uninstantiated Ancestor Nodes Marek J
... tive proba bilistic networks ( Druzdzel & Henrion, 1993; Henrion & Druzdzel, 1991), appr oximat e search-based algorithms for BBNs ( Henrion, 1991), and automatic generation of expl an ations of probabilistic reasoning in decision support systems (Druzdzel, 1993). Intercausal reasoning has been capt ...
... tive proba bilistic networks ( Druzdzel & Henrion, 1993; Henrion & Druzdzel, 1991), appr oximat e search-based algorithms for BBNs ( Henrion, 1991), and automatic generation of expl an ations of probabilistic reasoning in decision support systems (Druzdzel, 1993). Intercausal reasoning has been capt ...
Ergo: A Graphical Environment for Constructing Bayesian
... relationships among the variables. In particular, for each node Xi with a set of par ents 1ri, there is a conditional probability distribution P(xi I 1ri); for each Xi without parents, there is a prior probability distribution P(xv. Conditional probabilities in belief networks can be interpreted as ...
... relationships among the variables. In particular, for each node Xi with a set of par ents 1ri, there is a conditional probability distribution P(xi I 1ri); for each Xi without parents, there is a prior probability distribution P(xv. Conditional probabilities in belief networks can be interpreted as ...
Introduction to Sequence Analysis for Human Behavior
... The basic data structure used in the chapter is the graph. Definition 2.1 A graph is a data structure composed of a set of nodes and a set of edges. Two nodes can be connected by a directed or undirected edge. We will denote by G = (N, E) a graph, where N is the set of nodes and E is the set of the ...
... The basic data structure used in the chapter is the graph. Definition 2.1 A graph is a data structure composed of a set of nodes and a set of edges. Two nodes can be connected by a directed or undirected edge. We will denote by G = (N, E) a graph, where N is the set of nodes and E is the set of the ...
Entropy(Outlook)
... Example: After the outlook sunny node, we still can ask about temperature, humidity, and windiness. The humidity question has the best gain in entropy. ...
... Example: After the outlook sunny node, we still can ask about temperature, humidity, and windiness. The humidity question has the best gain in entropy. ...
Efficient Inference in Large Discrete Domains
... many of such pairs have negligible probabilities. In lan guage processing these models are represented (stored) us ing efficient N-gram decoding [Odell, Violative and Wood land, 1995] and hash table [Cohen, 1997]. Unfortunately these approaches do not extend to other domains such as the person id ...
... many of such pairs have negligible probabilities. In lan guage processing these models are represented (stored) us ing efficient N-gram decoding [Odell, Violative and Wood land, 1995] and hash table [Cohen, 1997]. Unfortunately these approaches do not extend to other domains such as the person id ...
While most ids systems reported in the literature use training data
... belief functions. That is, the current attribute to be selected is the attribute that maximizes information gain on the belief structure given the current training data set partition. The tree growing steps reiterate until we are out of attributes. Once we are done, outfitting may be eliminated usin ...
... belief functions. That is, the current attribute to be selected is the attribute that maximizes information gain on the belief structure given the current training data set partition. The tree growing steps reiterate until we are out of attributes. Once we are done, outfitting may be eliminated usin ...
A Decision Procedure for a Fragment of Linear Time Mu
... otherwise. A formula is called closed if it contains no free variables. We write [ 0 /Y ] for the result of simultaneously substituting 0 for all free occurrences of the variable Y in . For each variable X in a formula, we assume that X is bound at most once. Thus, it can be seen that all formulas c ...
... otherwise. A formula is called closed if it contains no free variables. We write [ 0 /Y ] for the result of simultaneously substituting 0 for all free occurrences of the variable Y in . For each variable X in a formula, we assume that X is bound at most once. Thus, it can be seen that all formulas c ...
Clustering by weighted cuts in directed graphs
... Markov chain, the data are mapped by X the eigenvectors of the transition matrix P = D −1 A. Therefore, when X has p.c columns, or near this case, the result can be interpreted in two equivalent ways. On one hand, the Markov chain can be aggregated according to clustering C ∗ without loss of informa ...
... Markov chain, the data are mapped by X the eigenvectors of the transition matrix P = D −1 A. Therefore, when X has p.c columns, or near this case, the result can be interpreted in two equivalent ways. On one hand, the Markov chain can be aggregated according to clustering C ∗ without loss of informa ...
An introduction to graphical models
... The following quotation, from the Preface of [Jor99], provides a very concise introduction to graphical models. Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and enginee ...
... The following quotation, from the Preface of [Jor99], provides a very concise introduction to graphical models. Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and enginee ...
Introduction to Artificial Intelligence – Course 67842
... States are defined by the values assigned so far. Initial state: the empty assignment { } Successor function: assign a value to an unassigned variable that does not conflict with current assignment fail if no legal assignments ...
... States are defined by the values assigned so far. Initial state: the empty assignment { } Successor function: assign a value to an unassigned variable that does not conflict with current assignment fail if no legal assignments ...
Logical and Probabilistic Knowledge Representation and Reasoning
... • The structure conveys causal elements • Conditional probabilities are initially given, and may be subjective • Additional assumptions ... ...
... • The structure conveys causal elements • Conditional probabilities are initially given, and may be subjective • Additional assumptions ... ...
Strong Cyclic Planning with Incomplete Information and Sensing
... that will be used to characterize the possible states of the world. The primitive fluents P may either be either predicates or terms containing variables ranging over finite domains, in such a way that the set of belief states B remains finite. Notice that these variables are typically used only for ...
... that will be used to characterize the possible states of the world. The primitive fluents P may either be either predicates or terms containing variables ranging over finite domains, in such a way that the set of belief states B remains finite. Notice that these variables are typically used only for ...
Introduction to AI
... • Example: the mutilated chess board problem. • A normal chess board has had two squares in opposite corners removed. Can you cover all the remaining squares exactly with dominoes? Each domino covers two square. No overlapping of dominoes, either on each other or over the boundary is allowed. ...
... • Example: the mutilated chess board problem. • A normal chess board has had two squares in opposite corners removed. Can you cover all the remaining squares exactly with dominoes? Each domino covers two square. No overlapping of dominoes, either on each other or over the boundary is allowed. ...
Knowledge representation
... What is the nature of truth? Artificial intelligence has also contributed to the theory of knowledge. Here is the view on knowledge adopted in Artificial intelligence, as described in Principia Cybernetica Web "Knowledge consists of models that attempt to represent the environment in such a way as ...
... What is the nature of truth? Artificial intelligence has also contributed to the theory of knowledge. Here is the view on knowledge adopted in Artificial intelligence, as described in Principia Cybernetica Web "Knowledge consists of models that attempt to represent the environment in such a way as ...
Modeling the probability of a binary outcome
... A linear classifier doesn't give us probabilities for the classes in any particular case. But we've seen that we often want such probabilities - to handle different error costs between classes, or to give us some indication of confidence for bet-hedging, or when perfect classification isn't possible ...
... A linear classifier doesn't give us probabilities for the classes in any particular case. But we've seen that we often want such probabilities - to handle different error costs between classes, or to give us some indication of confidence for bet-hedging, or when perfect classification isn't possible ...
Ontology of Actions
... all quantitative information can be handled on a ’lower’ level in the architecture. However the validity of this separation of levels has also often been questioned, and in the present lectures we shall start with the ’hybrid’ framework of both discrete and continuous state variables, and then consi ...
... all quantitative information can be handled on a ’lower’ level in the architecture. However the validity of this separation of levels has also often been questioned, and in the present lectures we shall start with the ’hybrid’ framework of both discrete and continuous state variables, and then consi ...
PDF
... In reinforcement learning, there is a tradeoff between spending time acting in the environment and spending time planning what actions are best. Model-free methods take one extreme on this question— the agent updates only the state most recently visited. On the other end of the spectrum lie classica ...
... In reinforcement learning, there is a tradeoff between spending time acting in the environment and spending time planning what actions are best. Model-free methods take one extreme on this question— the agent updates only the state most recently visited. On the other end of the spectrum lie classica ...
PowerPoint Presentation - Computing Science
... In some cases, as in the example above, inherited values may need to be overridden. (Fido may be a mammal, but if he’s male then he ...
... In some cases, as in the example above, inherited values may need to be overridden. (Fido may be a mammal, but if he’s male then he ...
Introduction to Sequence Analysis for Human Behavior Understanding
... The functions ϕc are often called potentials. They need to be positive functions but they do not necessarily need to be probabilities, i.e. they are not bound to range between 0 and 1. The conditional independence assumptions underlying the factorization above can be inferred by considering the defi ...
... The functions ϕc are often called potentials. They need to be positive functions but they do not necessarily need to be probabilities, i.e. they are not bound to range between 0 and 1. The conditional independence assumptions underlying the factorization above can be inferred by considering the defi ...
coherent knowledge processing at maximum entropy by spirit
... A similar approach to this form of knowledge representation can be found in the book of Hajek et al. (cf. [ 3] sec. 5). Some background in Probabilistic Logic (cf. [9]) would also be helpful for a better understanding of this paper. It's subject is the presentation of the shell SPIRIT and its way of ...
... A similar approach to this form of knowledge representation can be found in the book of Hajek et al. (cf. [ 3] sec. 5). Some background in Probabilistic Logic (cf. [9]) would also be helpful for a better understanding of this paper. It's subject is the presentation of the shell SPIRIT and its way of ...
Possibilistic conditional independence: A similarity
... All these methods have been applied using a single uncertainty formalism, i.e., probability. However, uncertainty about a domain can be due to other factors beyond those for which probability is adequate. When imprecision or ambiguity are inherent to the domain, possibility theory [11,20] is a good ...
... All these methods have been applied using a single uncertainty formalism, i.e., probability. However, uncertainty about a domain can be due to other factors beyond those for which probability is adequate. When imprecision or ambiguity are inherent to the domain, possibility theory [11,20] is a good ...
CSE 573 – Artificial Intelligence I – Autumn 2001
... 5. (a) Consider an arbitrary unit clause, say (p). What is the probability that a truth assignment chosen uniformly at random from the set of all truth assignments satisfies this clause? (b) Consider an arbitrary binary clause, say (p q). What is the probability that a randomly chosen truth assig ...
... 5. (a) Consider an arbitrary unit clause, say (p). What is the probability that a truth assignment chosen uniformly at random from the set of all truth assignments satisfies this clause? (b) Consider an arbitrary binary clause, say (p q). What is the probability that a randomly chosen truth assig ...
The importance of mixed selectivity in complex
... A majority of neurons are selective to at least 1 of the 3 task relevant aspects in 1 or more epochs. A large proportion also showed nonlinear-mixed selectivity a/b – a cell that is selective to a mixture of Cue1 identity and task-type. It responds to object C when presented as a first cue(more stro ...
... A majority of neurons are selective to at least 1 of the 3 task relevant aspects in 1 or more epochs. A large proportion also showed nonlinear-mixed selectivity a/b – a cell that is selective to a mixture of Cue1 identity and task-type. It responds to object C when presented as a first cue(more stro ...