Minimum Conditional Entropy Research Articles

Context quantization by kernel Fisher discriminant

Optimal context quantizers for minimum conditional entropy can be constructed by dynamic programming in the probability simplex space. The main difficulty, operationally, is the resulting complex quantizer mapping function in the context space, in which the conditional entropy coding is conducted. To overcome this difficulty, we propose new algorithms for designing context quantizers in the context space based on the multiclass Fisher discriminant and the kernel Fisher discriminant (KFD). In particular, the KFD can describe linearly nonseparable quantizer cells by projecting input context vectors onto a high-dimensional curve, in which these cells become better separable. The new algorithms outperform the previous linear Fisher discriminant method for context quantization. They approach the minimum empirical conditional entropy context quantizer designed in the probability simplex space, but with a practical implementation that employs a simple scalar quantizer mapping function rather than a large lookup table.

Monotonicity-Based Fast Algorithms for MAP Estimation of Markov Sequences Over Noisy Channels

In this correspondence, we study algorithmic approach to solving the problem of maximum a posteriori (MAP) estimation of Markov sequences transmitted over noisy channels, which is also known as the MAP decoding problem. For the class of memoryless binary channels that produce independent substitution and erasure errors, the MAP sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph. But for algorithm efficiency, we transform the graph problem to one of matrix search. If the underlying matrix is totally monotone, then the complexity of MAP sequence estimation can be greatly reduced. We give a sufficient condition for the matrix induced by MAP sequence estimation to be totally monotone, which is indeed the case if the input sequence is Gaussian Markov. Under this condition, the complexity of MAP decoding can be reduced from O(N/sup 2/M) to O(NM), where N is the size of source alphabet and M is the length of input sequence. Furthermore, for Markov sequences of fixed-length code we propose a block parsing strategy to reduce the complexity of MAP sequence estimation to O(M+N/sup 2/M/logM) or to O(M+NM/logM), depending on if the total monotonicity holds. Another significance of this correspondence lies in the applicability of the presented algorithmic approach, which has been thoroughly studied in computer science literature, to many other discrete optimization problems encountered in both source and channel coding, ranging from optimal multiresolution and multiple-description quantizer design, to context quantization for minimum conditional entropy, and to optimal packetization with uneven error protection.

Some Statistical-Estimation Methods for Stochastic Finite-State Transducers

Formal translations constitute a suitable framework for dealing with many problems in pattern recognition and computational linguistics. The application of formal transducers to these areas requires a stochastic extension for dealing with noisy, distorted patterns with high variability. In this paper, some estimation criteria are proposed and developed for the parameter estimation of regular syntax-directed translation schemata. These criteria are: maximum likelihood estimation, minimum conditional entropy estimation and conditional maximum likelihood estimation. The last two criteria were proposed in order to deal with situations when training data is sparse. These criteria take into account the possibility of ambiguity in the translations: i.e., there can be different output strings for a single input string. In this case, the final goal of the stochastic framework is to find the highest probability translation of a given input string. These criteria were tested on a translation task which has a high degree of ambiguity.

Structural and probabilistic knowledge for abductive reasoning

Different ways of representing probabilistic relationships among the attributes of a domain ar examined, and it is shown that the nature of domain relationships used in a representation affects the types of reasoning objectives that can be achieved. Two well-known formalisms for representing the probabilistic among attributes of a domain. These are the dependence tree formalism presented by C.K. Chow and C.N. Liu (1968) and the Bayesian networks methodology presented by J. Pearl (1986). An example is used to illustrate the nature of the relationships and the difference in the types of reasoning performed by these two representations. An abductive type of reasoning objective that requires use of the known qualitative relationships of the domain is demonstrated. A suitable way to represent such qualitative relationships along with the probabilistic knowledge is given, and how an explanation for a set of observed events may be constituted is discussed. An algorithm for learning the qualitative relationships from empirical data using an algorithm based on the minimization of conditional entropy is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>