Related papers: Multidimensional Projection Filters via Automatic …
Quantum embedding theories are playing an increasingly important role in bridging different levels of approximation to the many body Schr\"odinger equation in physics, chemistry and materials science. In this paper, we present a linear…
Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985)…
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
In the search for accurate approximate solutions of the many-body Schr\"odinger equation, reduced density matrices play an important role, as they allow to formulate approximate methods with polynomial scaling in the number of particles.…
Neural network pruning is a widely used strategy for reducing model storage and computing requirements. It allows to lower the complexity of the network by introducing sparsity in the weights. Because taking advantage of sparse matrices is…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Stochastic reaction networks (SRNs) model stochastic effects for various applications, including intracellular chemical or biological processes and epidemiology. A typical challenge in practical problems modeled by SRNs is that only a few…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration.…
We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations…
A numerical scheme for approximating the nonlinear filtering density is introduced and its convergence rate is established, theoretically under a parabolic H\"{o}rmander condition, and empirically in numerical examples. In a prediction…
Our proposal is on a new stochastic optimizer for non-convex and possibly non-smooth objective functions typically defined over large dimensional design spaces. Towards this, we have tried to bridge noise-assisted global search and faster…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
We introduce a framework for Data Assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data,…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…
Various particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes them an attractive alternative to traditional sequential Monte…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
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:…