Related papers: Multidimensional Projection Filters via Automatic …

We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) in this context turns into stochastic integrals with…

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…

We investigate the impact of filter choice on forecast accuracy in state space models. The filters are used both to estimate the posterior distribution of the parameters, via a particle marginal Metropolis-Hastings (PMMH) algorithm, and to…

One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a…

This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…

Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…

In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…

For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…

Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The…

We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…

We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…

Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…

We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be…

This work addresses the critical challenge of optimal filter selection for a novel trace gas measurement device. This device uses photonic crystal filters to retrieve trace gas concentrations affected by photon and read noise. The filter…

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…

Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…