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This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
Clinical prediction models must be developed using sufficiently large datasets to minimise overfitting and ensure robust predictive performance. Existing sample size calculations assume complete predictor data for all included participants,…
We propose a new approach to safe variable preselection in high-dimensional penalized regression, such as the lasso. Preselection - to start with a manageable set of covariates - has often been implemented without clear appreciation of its…
In recent years, there has been substantial interest in the task of selective inference: inference on a parameter that is selected from the data. Many of the existing proposals fall into what we refer to as the \emph{infer-and-widen}…
These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…
The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…
Given a reference model that includes all the available variables, projection predictive inference replaces its posterior with a constrained projection including only a subset of all variables. We extend projection predictive inference to…
New text as data techniques offer a great promise: the ability to inductively discover measures that are useful for testing social science theories of interest from large collections of text. We introduce a conceptual framework for making…
The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…
While reliable data-driven decision-making hinges on high-quality labeled data, the acquisition of quality labels often involves laborious human annotations or slow and expensive scientific measurements. Machine learning is becoming an…
Optimizing high-dimensional black-box functions under black-box constraints is a pervasive task in a wide range of scientific and engineering problems. These problems are typically harder than unconstrained problems due to hard-to-find…
We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Our intention is to provide a definitive reference on what it would take to safely make use of generative/predictive models in the absence of a solution to the Eliciting Latent Knowledge problem. Furthermore, we believe that large language…
The lasso is a popular method to induce shrinkage and sparsity in the solution vector (coefficients) of regression problems, particularly when there are many predictors relative to the number of observations. Solving the lasso in this…