Set Of Possible Hypotheses Research Articles

Sequential plan recognition: An iterative approach to disambiguating between hypotheses

Plan recognition algorithms output hypotheses about an agent's plans from its observed actions. Due to imperfect knowledge about the agent's behavior and the environment, it is often the case that there are multiple hypotheses about an agent's plans that are consistent with the observations, though only one of these hypotheses is correct. This paper addresses the problem of how to disambiguate between hypotheses during the recognition process, by querying the acting agent about whether a given plan is part of the correct hypothesis. The main contribution is a sound and complete process for reducing the set of possible hypotheses called Sequential Plan Recognition (SPR). SPR iteratively queries the user and revises the set of possible hypotheses according to the outcome of the query. Several policies are provided for choosing which plans to query the agent. These policies address the problem of how to reduce the number of hypotheses during the recognition process using a minimal number of queries. The proposed policies include policies that use maximum likelihood and information gain measures.The paper provides a complexity analysis of the SPR process and the proposed query policies. It demonstrate its efficiency on two known domains from the literature, describing how performance and runtime are affected by features in the domain. Our results can inform the design of future plan recognition systems that interleave the recognition process with intelligent interventions of their users.

Sparse Estimation of Polynomial and Rational Dynamical Models

In many practical situations, it is highly desirable to estimate an accurate mathematical model of a real system using as few parameters as possible. At the same time, the need for an accurate description of the system behavior without knowing its complete dynamical structure often leads to model parameterizations describing a rich set of possible hypotheses; an unavoidable choice, which suggests sparsity of the desired parameter estimate. An elegant way to impose this expectation of sparsity is to estimate the parameters by penalizing the criterion with the $\ell_{0}$ “norm” of the parameters. Due to the non-convex nature of the $\ell_{0}$ -norm, this penalization is often implemented as solving an optimization program based on a convex relaxation (e.g., $\ell_{1}$ /LASSO, nuclear norm, $\ldots$ ). Two difficulties arise when trying to apply these methods: (1) the need to use cross-validation or some related technique for choosing the values of regularization parameters associated with the $\ell_{1}$ penalty; and (2) the requirement that the (unpenalized) cost function must be convex. To address the first issue, we propose a new technique for sparse linear regression called SPARSEVA, with close ties with the LASSO (least absolute shrinkage and selection operator), which provides an automatic tuning of the amount of regularization. The second difficulty, which imposes a severe constraint on the types of model structures or estimation methods on which the $\ell_{1}$ relaxation can be applied, is addressed by combining SPARSEVA and the Steiglitz-McBride method. To demonstrate the advantages of the proposed approach, a solid theoretical analysis and an extensive simulation study are provided.

Rational variability in children’s causal inferences: The Sampling Hypothesis

We present a proposal—“The Sampling Hypothesis”—suggesting that the variability in young children’s responses may be part of a rational strategy for inductive inference. In particular, we argue that young learners may be randomly sampling from the set of possible hypotheses that explain the observed data, producing different hypotheses with frequencies that reflect their subjective probability. We test the Sampling Hypothesis with four experiments on 4- and 5-year-olds. In these experiments, children saw a distribution of colored blocks and an event involving one of these blocks. In the first experiment, one block fell randomly and invisibly into a machine, and children made multiple guesses about the color of the block, either immediately or after a 1-week delay. The distribution of guesses was consistent with the distribution of block colors, and the dependence between guesses decreased as a function of the time between guesses. In Experiments 2 and 3 the probability of different colors was systematically varied by condition. Preschoolers’ guesses tracked the probabilities of the colors, as should be the case if they are sampling from the set of possible explanatory hypotheses. Experiment 4 used a more complicated two-step process to randomly select a block and found that the distribution of children’s guesses matched the probabilities resulting from this process rather than the overall frequency of different colors. This suggests that the children’s probability matching reflects sophisticated probabilistic inferences and is not merely the result of a naïve tabulation of frequencies. Taken together the four experiments provide support for the Sampling Hypothesis, and the idea that there may be a rational explanation for the variability of children’s responses in domains like causal inference.

Sparse Estimation of Rational Dynamical Models

In many practical situations, it is highly desirable to estimate an accurate mathematical model of a real system using as few parameters as possible. This can be motivated either from appealing to a parsimony principle (Occam's razor) or from the view point of the utilization complexity in terms of control synthesis, prediction, etc. At the same time, the need for an accurate description of the system behavior without knowing its complete dynamical structure often leads to model parameterizations describing a rich set of possible hypotheses; an unavoidable choice, which suggests sparsity of the desired parameter estimate. An elegant way to impose this expectation of sparsity is to estimate the parameters by penalizing the criterion with the l0 norm of the parameters, which is often implemented as solving an optimization program based on a convex relaxation (e.g. l1/LASSO, nuclear norm, …). However, in order to apply these methods, the (unpenalized) cost function must be convex. This imposes a severe constraint on the types of model structures or estimation methods on which these relaxations can be applied. In this paper, we extend the use of convex relaxation techniques for sparsity to general rational plant model structures estimated by using prediction error minimization. This is done by combining the LASSO and the Steiglitz-McBride approaches. To demonstrate the advantages of the proposed solution an extensive simulation study is provided.

A computational model for auditory scene analysis

Primitive auditory scene analysis (ASA) is based on intrinsic properties of the auditory environment. Acoustic features such as continuity and proximity in time or frequency cause perceptual grouping of acoustic elements. Various grouping attributes have been translated into successful signal processing techniques that may be used in source separation. A next step beyond primitive ASA is source identification through schema‐based ASA. We present a computational model for ASA that is inspired by models from cognitive research. It dynamically builds a hierarchical network of hypotheses, which is based on (learned) knowledge of the sources. Each hypothesis in the network, initiated by bottom‐up evidence, represents a possible sound event. The network is updated for each new input event, which may be any sound in an unconstrained environment. The analysis of new input events is guided by knowledge of the environment and previous events. As a result of this adaptive behavior, information about the environment increases and the set of possible hypotheses decreases. With this method of continuously improving sound event identification we make a promising advance in computational ASA of complex real‐world environments.

Towards solving the multiple extension problem: Combining defaults and probabilities : Eric Neufeld and David Poole Logic Programming and Artificial Intelligence Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

The multiple extension problem frequently arises in both diagnostic and default reasoning. That is, in many settings it is possible to use any of a number of sets of instances defaults or hypotheses to explain (expected) observations. In some cases, we choose among explanations by making inferences about information believed to be implicit in the problem statement. If this isn't possible, we may still prefer one explanation to another because it is more likely or optimizes some other measureable property: cost, severity, fairness. We combine probabilities and defaults in a simple unified framework that retains the logical semantics of defaults and diagnosis as construction of explanations from a fixed set of possible hypotheses. We view probability as a property of an explanation that can be computed from a what is known and what is hypothesized by a valuation function. We present a procedure that performs an iterative deepening branch-and-bound search for explanations with the property that the first path found is the most likely. The procedure does not consider unlikely paths until more likely ones have been eliminated. We outline a way in which probabilities are not constrained by a priori independence assumptions; rather, these statistical assumptions are set up as defaults. While we use probability as a way of preferring one answer to another, the results apply to any property of an explanation having a valuation function meeting some usefulness criteria.

Learning complex rules in probabilistic inference tasks

Abstract.— A hypothesis‐sampling theory for rule learning predicts that only those rules that are available for sampling can be learned. Earlier results show that subjects have a very limited set of hypotheses about rules relating scaled cue and criterion variables, consisting mainly of linear and symmetric quadratic functions, but not of complex functions, such as J‐shaped rules. Tasks requiring the use of such rules should, therefore, not be learned. The results of the present experiment show, however, that subjects are able to find J‐shaped relations. The results were interpreted to mean that subjects are able to construct hypotheses, and that they are not limited to sampling of hypotheses from a preestablished set of possible hypotheses.

Detection and prediction of a stochastic process having multiple hypotheses

A system is proposed which combines hypothesis testing and prediction to estimate the future value of a stochastic process whose statistics are known only to belong to some finite set of possible hypotheses. Bayes optimization of the individual components is performed, and system performance is discussed for a modified version of the usual mean-squared error predictor cost functions. An example is given illustrating various features of the system's performance for a specific choice of input hypotheses.