Objective methods for assessing perceptual image quality traditionally attempted to quantify the visibility of errors (differences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative …

General formulation of the problem; Important examples; Black box and iterative methods; Analytical and arithmetical complexity; Uniform grid method; Lower complexity bounds; Lower bounds for global optimization; Rules of the game.

Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this …

In this paper we present a new notion of curvature for cell complexes. For each p, we define a pth combinatorial curvature function, which assigns a number to each p-cell of the complex. The curvature of a p-cell depends only on the relationships between the cell and its neighbors. In the case that p = 1, the curvature function appears to play the role for cell complexes that Ricci curvature plays …

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the …

We propose a modular reinforcement learning architecture for nonlinear, nonstationary control tasks, which we call multiple model-based reinforcement learning (MMRL). The basic idea is to decompose a complex task into multiple domains in space and time based on the predictability of the environmental dynamics. The system is composed of multiple modules, each of which consists of a state prediction …

This paper reviews the supervised learning versions of the no-free-lunch theorems in a simplified form. It also discusses the significance of those theorems, and their relation to other aspects of supervised learning.

We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the parameter space. Although gradient methods cannot make large changes in the values of the parameters, we show that the natural gradient is moving toward choosing a greedy optimal action rather than just a better action. These greedy optimal actions are those that would be …

We present conditional random fields, a framework for building probabilistic models to segment and label sequence data. Conditional random fields offer several advantages over hidden Markov models and stochastic grammars for such tasks, including the ability to relax strong independence assumptions made in those models. Conditional random fields also avoid a fundamental limitation of maximum entropy …

Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. The article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a …

For many KDD applications, such as detecting criminal activities in E-commerce, finding the rare instances or the outliers, can be more interesting than finding the common patterns. Existing work in outlier detection regards being an outlier as a binary property. In this paper, we contend that for many scenarios, it is more meaningful to assign to each object a degree of being an outlier. This …

This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization. Written primarily for …

The output of a classifier should be a calibrated posterior probability to enable post-processing. Standard SVMs do not provide such probabilities. One method to create probabilities is to directly train a kernel classifier with a logit link function and a regularized maximum likelihood score. However, training with a maximum likelihood score will produce non-sparse kernel machines. Instead, we …

Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, independent of the value function, and is updated according to the …

We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial/boundary conditions. This part involves a feedforward neural …

The generalized Pareto distribution (GPD) was introduced by Pickands to model exceedances over a threshold. It has since been used by many authors to model data in several fields. The GPD has a scale parameter (\[sgrave] > 0) and a shape parameter (−∞ < k < ∞). The estimation of these parameters is not generally an easy problem. When k > 1, the maximum likelihood estimates do not exist, and when k …

The purpose of this paper is to investigate neural network capability systematically. The main results are: 1) every Tauber-Wiener function is qualified as an activation function in the hidden layer of a three-layered neural network; 2) for a continuous function to be a Tauber-Wiener function, the necessary and sufficient condition is that it is not a polynomial; 3) the capability of approximating …

One of the key factors which limits the use of neural networks in many industrial applications has been the difficulty of demonstrating that a trained network will continue to generate reliable outputs once it is in routine use. An important potential source of errors is novel input data; that is, input data which differ significantly from the data used to train the network. The author …

A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for …

This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is …

Let Wt; t ϵ [0, 1] be a standard k-dimensional Weiner process defined on a probability space (Ω, F, P), and let Ft denote its natural filtration. Given a F1 measurable d-dimensional random vector X, we look for an adapted pair of processes {x(t), y(t); t ϵ [0, 1]} with values in Rd and Rd×k respectively, which solves an equation of the form: x(t) + ∫t1f(s, x(s), y(s)) ds + ∫t1 [g(s, x(s)) + y(s)] …

A common reaction among applied statisticians is that the Bayesian statistician's energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying Bayes's theorem to calculate conditional distributions of unknowns given knowns. I feel, however, that the applied Bayesian …

Suppose that a forecaster sequentially assigns probabilities to events. He is well calibrated if, for example, of those events to which he assigns a probability 30 percent, the long-run proportion that actually occurs turns out to be 30 percent. We prove a theorem to the effect that a coherent Bayesian expects to be well calibrated, and consider its destructive implications for the theory of …

Reverse-time stochastic diffusion equation models are defined and it is shown how most processes defined via a forward-time or conventional diffusion equation model have an associated reverse-time model.

Any applied statistician who has analysed a number of sets of real data is likely to have come across ‘outliers’. The intuitive definition of an outlier would be ‘an observation which deviates so much from other observations as to arouse suspicions that it was generated by a different mechanism’. An inspection of a sample containing outliers would show up such characteristics as large gaps between …

This paper treats essentially the first derivative of an estimator viewed as functional and the ways in which it can be used to study local robustness properties. A theory of robust estimation "near" strict parametric models is briefly sketched and applied to some classical situations. Relations between von Mises functionals, the jackknife and U-statistics are indicated. A number of classical and …

A FORTRAN subroutine is described for minimizing a sum of squares of functions of many variables. Such problems arise in non-linear data fitting, and in the solution of non-linear algebraic equations. The subroutine is based on an algorithn due to Marquardt, but with modifications which improve the performance of the method in certain circumstances, yet which require negligible extra computer time …