Related papers: Risk and cross validation in ridge regression with…
We consider distributed learning using constant stepsize SGD (DSGD) over several devices, each sending a final model update to a central server. In a final step, the local estimates are aggregated. We prove in the setting of…
Agent-Based Model (ABM) validation is crucial as it helps ensuring the reliability of simulations, and causal discovery has become a powerful tool in this context. However, current causal discovery methods often face accuracy and robustness…
We prove theorems about the Gaussian asymptotics of an empirical bridge built from linear model regressors with multiple regressor ordering. We study the testing of the hypothesis of a linear model for the components of a random vector: one…
Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of…
Kernel ridge regression, KRR, is a generalization of linear ridge regression that is non-linear in the data, but linear in the model parameters. Here, we introduce an equivalent formulation of the objective function of KRR, which opens up…
We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…
Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a…
We propose a novel approach for domain generalisation (DG) leveraging risk distributions to characterise domains, thereby achieving domain invariance. In our findings, risk distributions effectively highlight differences between training…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating…
The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
When assessing risks on a finite-time horizon, the problem can often be reduced to the study of a random sequence $C(N)=(C_1,\ldots,C_N)$ of random length $N$, where $C(N)$ comes from the product of a matrix $A(N)$ of random size $N \times…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…
The use of cumulative incidence functions for characterizing the risk of one type of event in the presence of others has become increasingly popular over the past decade. The problems of modeling, estimation and inference have been treated…
Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions,…
In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal…
We consider standard gradient descent, gradient flow and conjugate gradients as iterative algorithms for minimising a penalised ridge criterion in linear regression. While it is well known that conjugate gradients exhibit fast numerical…
In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also,…
As opaque predictive models increasingly impact many areas of modern life, interest in quantifying the importance of a given input variable for making a specific prediction has grown. Recently, there has been a proliferation of…