Related papers: On Learning the Optimal Regularization Parameter i…

We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to…

In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The…

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning…

We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

We consider the statistical inverse problem to recover $f$ from noisy measurements $Y = Tf + \sigma \xi$ where $\xi$ is Gaussian white noise and $T$ a compact operator between Hilbert spaces. Considering general reconstruction methods of…

We propose a supervised learning approach for predicting an underlying graph from a set of graph signals. Our approach is based on linear regression. In the linear regression model, we predict edge-weights of a graph as the output, given a…

In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…

How can we effectively remove or ''unlearn'' undesirable information, such as specific features or the influence of individual data points, from a learning outcome while minimizing utility loss and ensuring rigorous guarantees? We introduce…

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…

Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the…

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…

The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…