This paper proposes a practical optimization method for layered neural networks, by which the optimal model and parameter can be found simultaneously. 'i\Te modify the conventional information criterion into a differentiable function of parameters, and then, min(cid:173) imize it, while controlling it back to the ordinary form. Effective(cid:173) ness of this method is discussed theoretically and experimentally.

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learn(cid:173) ing problems involving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DP-based learning algorithms to the pow(cid:173) erful techniques of stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD(") and Q-Iearning belong.

Transition point dynamic programming (TPDP) is a memory(cid:173) based, reinforcement learning, direct dynamic programming ap(cid:173) proach to adaptive optimal control that can reduce the learning time and memory usage required for the control of continuous stochastic dynamic systems. TPDP does so by determining an ideal set of transition points (TPs) which specify only the control action changes necessary for optimal control. TPDP converges to an ideal TP set by using a variation of Q-Iearning to assess the mer(cid:173) its of adding, swapping and removing TPs from states throughout the state space. When applied to a race track problem, TPDP learned the optimal control policy much sooner than conventional Q-Iearning, and was able to do so using less memory.

We consider the solution to large stochastic control problems by means of methods that rely on compact representations and a vari(cid:173) ant of the value iteration algorithm to compute approximate cost(cid:173) to-go functions. While such methods are known to be unstable in general, we identify a new class of problems for which convergence, as well as graceful error bounds, are guaranteed. This class in(cid:173) volves linear parameterizations of the cost-to- go function together with an assumption that the dynamic programming operator is a contraction with respect to the Euclidean norm when applied to functions in the parameterized class. We provide a special case where this assumption is satisfied, which relies on the locality of transitions in a state space. Other cases will be discussed in a full length version of this paper.

A new learning algorithm is developed for the design of statistical classifiers minimizing the rate of misclassification. The method, which is based on ideas from information theory and analogies to statistical physics, assigns data to classes in probability. The dis(cid:173) tributions are chosen to minimize the expected classification error while simultaneously enforcing the classifier's structure and a level of "randomness" measured by Shannon's entropy. Achievement of the classifier structure is quantified by an associated cost. The con(cid:173) strained optimization problem is equivalent to the minimization of a Helmholtz free energy, and the resulting optimization method is a basic extension of the deterministic annealing algorithm that explicitly enforces structural constraints on assignments while re(cid:173) ducing the entropy and expected cost with temperature.

Belief networks are graphical representations of probability distributions over a set of variables. In what follows it will be always assumed that the variables take values in a finite set and that they correspond to the vertices of a graph. The graph's arcs will represent the dependencies among variables. There are two kinds of representations that have gained wide use: one is the directed acyclic graph model, also called a Bayes net, which represents the joint distribution as a product of the probabilities of each vertex conditioned on the values of its parents; the other is the undirected graph model, also called a Markov field, where the joint distribution is factorized over the cliques! of an undirected graph. This factorization is called a junction tree and optimizing it is the subject of the present paper. The power of both models lies in their ability to display and exploit existent marginal and conditional independencies among subsets of variables.

In many optimization problems, the structure of solutions reflects complex relationships between the different input parameters. For example, experience may tell us that certain parameters are closely related and should not be explored independently. Similarly, ex(cid:173) perience may establish that a subset of parameters must take on particular values. Any search of the cost landscape should take advantage of these relationships. We present MIMIC, a framework in which we analyze the global structure of the optimization land(cid:173) scape. A novel and efficient algorithm for the estimation of this structure is derived.

Output coding is a general method for solving multiclass problems by reducing them to multiple binary classification problems. Previous re(cid:173) search on output coding has employed, almost solely, predefined discrete codes. We describe an algorithm that improves the performance of output codes by relaxing them to continuous codes. The relaxation procedure is cast as an optimization problem and is reminiscent of the quadratic program for support vector machines. We describe experiments with the proposed algorithm, comparing it to standard discrete output codes.

The paper presents a novel technique of constrained independent component analysis (CICA) to introduce constraints into the clas(cid:173) sical ICA and solve the constrained optimization problem by using Lagrange multiplier methods. This paper shows that CICA can be used to order the resulted independent components in a specific manner and normalize the demixing matrix in the signal separation procedure. It can systematically eliminate the ICA's indeterminacy on permutation and dilation. The experiments demonstrate the use of CICA in ordering of independent components while providing normalized demixing processes.

Novelty detection involves modeling the normal behaviour of a sys(cid:173) tem hence enabling detection of any divergence from normality. It has potential applications in many areas such as detection of ma(cid:173) chine damage or highlighting abnormal features in medical data. One approach is to build a hypothesis estimating the support of the normal data i.e. constructing a function which is positive in the region where the data is located and negative elsewhere. Recently kernel methods have been proposed for estimating the support of a distribution and they have performed well in practice - training involves solution of a quadratic programming problem. In this pa(cid:173) per we propose a simpler kernel method for estimating the support based on linear programming.