arXiv research

New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.

Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.

We outline new approaches to incorporate ideas from deep learning into wave-based least-squares imaging. The aim, and main contribution of this work, is the combination of handcrafted constraints with deep convolutional neural networks, as a way to harness their remarkable ease of generating natural images. The mathema…

Identifies interpretable generative model for multivariate data.

This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common \textit{noise conditions}. These rates display interesting transitions -- due to the inte…

Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univa…

Theory for soft-margin classifiers on object manifolds.

In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step process: first, using system identification tools rooted in subspace methods, we ob…

The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.

The study establishes SQ lower bounds for learning halfspaces and ReLUs under Gaussian marginals.

Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically either uses MCMC schemes which target the joint posterior of the parameters and some…

We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. By minimizing a hinge-loss using the linear expectation operat…

New method models unknown systems with hidden parameters using neural networks.

This paper offers a simple method for Bayesian regression with unknown transformations.

Paper analyzes GMM for separable data with various parameter structures.

We consider a problem of multiclass classification, where the training sample $S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb P(Y = m | X = x) = η_m(x)$, $1 \leq m \leq M$, and $η_1(x), \dots, η_M(x)$ are unknown $α$-Holder continuous functions.Given a test point $X$, our goal is to predict its labe…

Efficient algorithm predicts unknown linear systems with long-term memory.

Optimizes risk measures given known marginal distributions of two unknown factors.

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalm…

In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…

Novel proof shows continuity of optimal transport feasible set mapping.

We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical s…

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted…

Bayesian framework integrates prior and data knowledge for nonlinear dynamical systems.

Algorithm learns dynamics from past observations.

Audited Conformal Prediction improves conditional coverage in pretrained models under distribution shift.

This paper solves robust utility maximization with unknown claim dependencies.

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based met…

Bayesian method synthesizes barrier certificates for unknown systems with latent states.

New method selects variables for GP regression using sparse projection.

Estimates high-dimensional posterior densities by marginal distributions and neural networks.

Latent Dirichlet allocation (LDA) is useful in document analysis, image processing, and many information systems; however, its generalization performance has been left unknown because it is a singular learning machine to which regular statistical theory can not be applied. Stochastic matrix factorization (SMF) is a res…

Identifying components and estimating mixing weights in unlabeled finite mixtures under marginal independence.

The paper develops a method to infer model parameters and shared dynamics from related physical systems using data.

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By failure we mean that th…

New BED method handles online inference for partially observed dynamical systems.

New algorithm reduces bandit problem's regret bound to logarithmic in dimension.

Study strategic dynamic pricing for buyers with unknown manipulation costs.

Efficient algorithms improve learning of large-margin halfspaces.

New method identifies drift and diffusivity from SDE marginals.

Paper develops PAC-Bayes bounds for unknown linear systems.

Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo, combining MCMC and sequential Monte Carlo to form "exact approximations" to otherwise intractable MCMC methods. The performance of the approximation is limited to t…

Paper solves stock loan pricing with finite maturity using integral equations.

Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function throug…

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the u…

OPNP prunes parameters and neurons to improve OOD detection without training.

Efficiently estimates marginal posteriors for complex simulations.