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Inferring unknown conic sections on the basis of noisy data is a challenging problem with applications in computer vision. A major limitation of the currently available methods for conic sections is that estimation methods rely on the…

There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Accurate acoustic simulations of enclosed spaces require precise boundary conditions, typically expressed through surface impedances for wave-based methods. Conventional measurement techniques often rely on simplifying assumptions about the…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…

This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

We focus on using the predictive uncertainty signal calculated by Bayesian neural networks to guide learning in the self-same task the model is being trained on. Not opting for costly Monte Carlo sampling of weights, we propagate the…

Smoothing splines can be thought of as the posterior mean of a Gaussian process regression in a certain limit. By constructing a reproducing kernel Hilbert space with an appropriate inner product, the Bayesian form of the V-spline is…

Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate…

Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate…

Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…

Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have…

This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…

In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…

In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding…

We consider the problem of estimating a parameter associated to a Bayesian inverse problem. Treating the unknown initial condition as a nuisance parameter, typically one must resort to a numerical approximation of gradient of the…