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In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
Missing data is a common issue in real-world datasets. This paper studies the performance of impute-then-regress pipelines by contrasting theoretical and empirical evidence. We establish the asymptotic consistency of such pipelines for a…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…
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…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
Fault-tolerant quantum computing will require accurate estimates of the resource overhead, but standard metrics such as gate fidelity and diamond distance have been shown to be poor predictors of logical performance. We present a scalable…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…
We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT.…
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the…
Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient…
This paper introduces a new technique for quantifying the approximation error of a broad class of probabilistic inference programs, including ones based on both variational and Monte Carlo approaches. The key idea is to derive a subjective…
A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyze the minimum-error protocol…
Quantum Hypothesis Testing has shown the advantages that quantum resources can offer in the discrimination of competing hypothesis. Here, we apply this framework to optomechanical systems and fundamental physics questions. In particular, we…
We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the…
Quantification of Uncertainty in predictions is a challenging problem. In the classification settings, although deep learning based models generalize well, class probabilities often lack reliability. Calibration errors are used to quantify…