Related papers: Optimal Partitions for Nonparametric Multivariate …
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium.…
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…
In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we…
Sampling is often a necessary evil to reduce the processing and storage costs of distributed tracing. In this work, we describe a scalable and adaptive sampling approach that can preserve events of interest better than the widely used…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
To cope with fast-fluctuating distributed energy resources (DERs) and uncontrolled loads, this paper formulates a time-varying optimization problem for distribution grids with DERs and develops a novel non-iterative algorithm to track the…
We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs).…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distribution. However, when the problem exhibits certain kind of…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile method to estimate rare events probabilities. It is an iterative procedure on an interacting particle system, where at each step, the $k$ less well-adapted…
Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient…