Related papers: Piecewise Convex Function Estimation and Model Sel…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
A number of results related to statistical classification on convex sets are presented. In particular, the focus is on the case where some of the covariates in the data and observation being classified can be missing. The form of the…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
Segmentation is a fundamental task in medical image analysis. The clinical interest is often to measure the volume of a structure. To evaluate and compare segmentation methods, the similarity between a segmentation and a predefined ground…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…
Recent progress in robotic manipulation has dealt with the case of previously unknown objects in the context of relatively simple tasks, such as bin-picking. Existing methods for more constrained problems, however, such as deliberate…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…