Related papers: Indeterminate Probability Theory
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different…
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently…
Uncertainty quantification for individual treatment effects (ITEs) is a daunting challenge in causal inference. Motivated by recent advances in conformal prediction, several works aim to construct distribution-free prediction sets for ITEs…
In various applications, probabilistic forecasts are required to quantify the inherent uncertainty associated with the forecast. However, numerous modern forecasting methods are still designed to create deterministic forecasts. Transforming…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for…
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…
This paper develops an updatable inverse probability weighting (UIPW) estimation for the generalized linear models with response missing at random in streaming data sets. A two-step online updating algorithm is provided for the proposed…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
In the probabilistic approach to uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability…
Probabilistic databases (PDBs) model uncertainty in data. The current standard is to view PDBs as finite probability spaces over relational database instances. Since many attributes in typical databases have infinite domains, such as…
Temporal Point Processes (TPP) play an important role in predicting or forecasting events. Although these problems have been studied extensively, predicting multiple simultaneously occurring events can be challenging. For instance, more…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…