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We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to…
Despite impressive performance as evaluated on i.i.d. holdout data, deep neural networks depend heavily on superficial statistics of the training data and are liable to break under distribution shift. For example, subtle changes to the…
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…
Sparse training is a natural idea to accelerate the training speed of deep neural networks and save the memory usage, especially since large modern neural networks are significantly over-parameterized. However, most of the existing methods…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of…
Learning surfaces from neural radiance field (NeRF) became a rising topic in Multi-View Stereo (MVS). Recent Signed Distance Function (SDF)-based methods demonstrated their ability to reconstruct accurate 3D shapes of Lambertian scenes.…
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the L1/Lq norm with q > 1 is attractive in many applications of…
In this paper, we present a new variational method for sparse regression using $L_0$ regularization. The variational parameters appear in the approximate model in a way that is similar to Breiman's Garrote model. We refer to this method as…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
We propose a few-shot learning method for spatial regression. Although Gaussian processes (GPs) have been successfully used for spatial regression, they require many observations in the target task to achieve a high predictive performance.…
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…
In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel stochastic method -- Orthant Based Proximal Stochastic…