Related papers: Group Invariance and Computational Sufficiency
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…
*Minimal sufficient reasons* represent a prevalent form of explanation - the smallest subset of input features which, when held constant at their corresponding values, ensure that the prediction remains unchanged. Previous *post-hoc*…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of…
We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as Column Subset Selection (CSS).…
Gaussian processes (GP) are attractive building blocks for many probabilistic models. Their drawbacks, however, are the rapidly increasing inference time and memory requirement alongside increasing data. The problem can be alleviated with…
We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
We consider computationally-efficient estimation of population parameters when observations are subject to missing data. In particular, we consider estimation under the realizable contamination model of missing data in which an $\epsilon$…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…
We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…