11,199 research outputs found
CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis
We propose and evaluate a new technique for learning hybrid automata
automatically by observing the runtime behavior of a dynamical system. Working
from a sequence of continuous state values and predicates about the
environment, CHARDA recovers the distinct dynamic modes, learns a model for
each mode from a given set of templates, and postulates causal guard conditions
which trigger transitions between modes. Our main contribution is the use of
information-theoretic measures (1)~as a cost function for data segmentation and
model selection to penalize over-fitting and (2)~to determine the likely causes
of each transition. CHARDA is easily extended with different classes of model
templates, fitting methods, or predicates. In our experiments on a complex
videogame character, CHARDA successfully discovers a reasonable
over-approximation of the character's true behaviors. Our results also compare
favorably against recent work in automatically learning probabilistic timed
automata in an aircraft domain: CHARDA exactly learns the modes of these
simpler automata.Comment: 7 pages, 2 figures. Accepted for IJCAI 201
Rational stochastic languages
The goal of the present paper is to provide a systematic and comprehensive
study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A
rational stochastic language is a probability distribution over a free monoid
\Sigma^* which is rational over K, that is which can be generated by a
multiplicity automata with parameters in K. We study the relations between the
classes of rational stochastic languages S rat K (\Sigma). We define the notion
of residual of a stochastic language and we use it to investigate properties of
several subclasses of rational stochastic languages. Lastly, we study the
representation of rational stochastic languages by means of multiplicity
automata.Comment: 35 page
Learning probability distributions generated by finite-state machines
We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference
in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft
Calibrating Generative Models: The Probabilistic Chomsky-SchĂĽtzenberger Hierarchy
A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning
PAC Classification based on PAC Estimates of Label Class Distributions
A standard approach in pattern classification is to estimate the
distributions of the label classes, and then to apply the Bayes classifier to
the estimates of the distributions in order to classify unlabeled examples. As
one might expect, the better our estimates of the label class distributions,
the better the resulting classifier will be. In this paper we make this
observation precise by identifying risk bounds of a classifier in terms of the
quality of the estimates of the label class distributions. We show how PAC
learnability relates to estimates of the distributions that have a PAC
guarantee on their distance from the true distribution, and we bound the
increase in negative log likelihood risk in terms of PAC bounds on the
KL-divergence. We give an inefficient but general-purpose smoothing method for
converting an estimated distribution that is good under the metric into a
distribution that is good under the KL-divergence.Comment: 14 page
Complexity of Equivalence and Learning for Multiplicity Tree Automata
We consider the complexity of equivalence and learning for multiplicity tree
automata, i.e., weighted tree automata over a field. We first show that the
equivalence problem is logspace equivalent to polynomial identity testing, the
complexity of which is a longstanding open problem. Secondly, we derive lower
bounds on the number of queries needed to learn multiplicity tree automata in
Angluin's exact learning model, over both arbitrary and fixed fields.
Habrard and Oncina (2006) give an exact learning algorithm for multiplicity
tree automata, in which the number of queries is proportional to the size of
the target automaton and the size of a largest counterexample, represented as a
tree, that is returned by the Teacher. However, the smallest
tree-counterexample may be exponential in the size of the target automaton.
Thus the above algorithm does not run in time polynomial in the size of the
target automaton, and has query complexity exponential in the lower bound.
Assuming a Teacher that returns minimal DAG representations of
counterexamples, we give a new exact learning algorithm whose query complexity
is quadratic in the target automaton size, almost matching the lower bound, and
improving the best previously-known algorithm by an exponential factor
POMDPs under Probabilistic Semantics
We consider partially observable Markov decision processes (POMDPs) with
limit-average payoff, where a reward value in the interval [0,1] is associated
to every transition, and the payoff of an infinite path is the long-run average
of the rewards. We consider two types of path constraints: (i) quantitative
constraint defines the set of paths where the payoff is at least a given
threshold lambda_1 in (0,1]; and (ii) qualitative constraint which is a special
case of quantitative constraint with lambda_1=1. We consider the computation of
the almost-sure winning set, where the controller needs to ensure that the path
constraint is satisfied with probability 1. Our main results for qualitative
path constraint are as follows: (i) the problem of deciding the existence of a
finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding
the existence of an infinite-memory controller is undecidable. For quantitative
path constraint we show that the problem of deciding the existence of a
finite-memory controller is undecidable.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Inducing Probabilistic Grammars by Bayesian Model Merging
We describe a framework for inducing probabilistic grammars from corpora of
positive samples. First, samples are {\em incorporated} by adding ad-hoc rules
to a working grammar; subsequently, elements of the model (such as states or
nonterminals) are {\em merged} to achieve generalization and a more compact
representation. The choice of what to merge and when to stop is governed by the
Bayesian posterior probability of the grammar given the data, which formalizes
a trade-off between a close fit to the data and a default preference for
simpler models (`Occam's Razor'). The general scheme is illustrated using three
types of probabilistic grammars: Hidden Markov models, class-based -grams,
and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second
International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13
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