Related papers: Convex Nonparanormal Regression
Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive family of meta-learning models which produce well-calibrated predictions, enable fast inference at test time, and are trainable via a simple maximum likelihood…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Conditional Neural Processes~(CNPs) bridge neural networks with probabilistic inference to approximate functions of Stochastic Processes under meta-learning settings. Given a batch of non-{\it i.i.d} function instantiations, CNPs are…
An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…
Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can…
Conditional Neural Processes~(CNPs) formulate distributions over functions and generate function observations with exact conditional likelihoods. CNPs, however, have limited expressivity for high-dimensional observations, since their…
Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability…
Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly…
The history of the seemingly simple problem of straight line fitting in the presence of both $x$ and $y$ errors has been fraught with misadventure, with statistically ad hoc and poorly tested methods abounding in the literature. The problem…
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the…
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…
Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…
Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in…
Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
High-dimensional inference methods often rely on coefficient sparsity, an assumption that can be restrictive when signals are dense but individually weak. In such settings, valid inference may still be possible if the covariates exhibit…