Related papers: Exact Minimum-Volume Confidence Set Intersection f…
Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. This paper studies the geometry of the…
Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…
Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider…
We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S…
In this article, we introduce the concept of model confidence bounds (MCB) for variable selection in the context of nested models. Similarly to the endpoints in the familiar confidence interval for parameter estimation, the MCB identifies…
Determining the number of change-points is a first-step and fundamental task in change-point detection problems, as it lays the groundwork for subsequent change-point position estimation. While the existing literature offers various methods…
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure…
The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities. In this paper, we resolve two longstanding open problems on bounding the…
Linear combinations of multinomial probabilities, such as those resulting from contingency tables, are of use when evaluating classification system performance. While large sample inference methods for these combinations exist, small sample…
This paper proposes vehicle motion planning methods with obstacle avoidance in tight spaces by incorporating polygonal approximations of both the vehicle and obstacles into a model predictive control (MPC) framework. Representing these…
The hypervolume indicator is one of the most used set-quality indicators for the assessment of stochastic multiobjective optimizers, as well as for selection in evolutionary multiobjective optimization algorithms. Its theoretical properties…
Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set…
Memory consistency models (MCMs) which govern inter-module interactions in a shared memory system, are a significant, yet often under-appreciated, aspect of system design. MCMs are defined at the various layers of the hardware-software…
In this work, we study two fundamental graph optimization problems, minimum vertex cover (MVC) and maximum-cardinality matching (MCM), for intersection graphs of geometric objects, e.g., disks, rectangles, hypercubes, etc., in…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…
Economic models produce moment inequalities, which can be used to form tests of the true parameters. Confidence sets (CS) of the true parameters are derived by inverting these tests. However, they often lack analytical expressions,…
Multimodal AI systems are evaluated by downstream task accuracy, but high accuracy does not mean the underlying data is coherent. A model can score well on Visual Question Answering (VQA) while its inputs contradict each other. We introduce…
A fundamental challenge in approximating an unknown density using finite Gaussian mixture models is selecting the number of mixture components, also known as order. Traditional approaches choose a single best model using information…
As a technique that can compactly represent complex patterns, machine learning has significant potential for predictive inference. K-fold cross-validation (CV) is the most common approach to ascertaining the likelihood that a machine…
End member analysis (EMA) unmixes grain size distribution (GSD) data into a mixture of end members (EMs), thus helping understand sediment provenance and depositional regimes and processes. In highly mixed data sets, however, many EMA…