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Simulation-based inference provides a powerful framework for Bayesian inference when the likelihood is analytically intractable or computationally prohibitive. By leveraging machine-learning techniques and neural density estimators, it…
The recent decade has seen an enormous rise in the popularity of deep learning and neural networks. These algorithms have broken many previous records and achieved remarkable results. Their outstanding performance has significantly sped up…
Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both…
We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…
Understanding theoretical properties of deep and locally connected nonlinear network, such as deep convolutional neural network (DCNN), is still a hard problem despite its empirical success. In this paper, we propose a novel theoretical…
Deep neural networks (DNNs) have successfully learned useful data representations in various tasks. However, assessing the reliability of these representations remains a challenge. Deep Ensemble is widely considered the state-of-the-art…
The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…
There has been a significant recent surge in deep neural network (DNN) techniques. Most of the existing DNN techniques have restricted model formats/assumptions. To overcome their limitations, we propose the nonparametric transformation…
Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting…
Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations…
We bound the excess risk of interpolating deep linear networks trained using gradient flow. In a setting previously used to establish risk bounds for the minimum $\ell_2$-norm interpolant, we show that randomly initialized deep linear…
The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work…
Temporal prediction is inherently uncertain, but representing the ambiguity in natural image sequences is a challenging high-dimensional probabilistic inference problem. For natural scenes, the curse of dimensionality renders explicit…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…
We exploit recent results in quantifying the robustness of neural networks to input variations to construct and tune a model-based anomaly detector, where the data-driven estimator model is provided by an autoregressive neural network. In…
We study variance estimation and associated confidence intervals for parameters characterizing genetic effects from genome-wide association studies (GWAS) misspecified mixed model analysis. Previous studies have shown that, in spite of the…
We prove a large deviation principle for deep neural networks with Gaussian weights and at most linearly growing activation functions, such as ReLU. This generalises earlier work, in which bounded and continuous activation functions were…
We study the approximation of the median of $d$ inputs using ReLU neural networks. We present depth-width tradeoffs under several settings, culminating in a constant-depth, linear-width construction that achieves exponentially small…