Related papers: Optimal discriminating designs for several competi…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
In a tie-breaker design (TBD), subjects with high values of a running variable are given some (usually desirable) treatment, subjects with low values are not, and subjects in the middle are randomized. TBDs are intermediate between…
Artificial neural networks have gone through a recent rise in popularity, achieving state-of-the-art results in various fields, including image classification, speech recognition, and automated control. Both the performance and…
Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
In a seminal paper \cite{studden1968} characterized $c$-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual…
Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…
Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional…
We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate $\hat{\beta}$ of the hidden parameter $\beta^{\star}$ of an underlying linear model. The key…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…
Efficient algorithms for searching for optimal saturated designs are widely available. They maximize a given efficiency measure (such as D-optimality) and provide an optimum design. Nevertheless, they do not guarantee a \emph{global}…
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…
Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating…
We propose a new family of label randomizers for training regression models under the constraint of label differential privacy (DP). In particular, we leverage the trade-offs between bias and variance to construct better label randomizers…
The problem of reward design examines the interaction between a leader and a follower, where the leader aims to shape the follower's behavior to maximize the leader's payoff by modifying the follower's reward function. Current approaches to…
This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An $l_1$ minimization method is used to select the…
The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…