Related papers: Probability Bracket Notation for Probability Model…
This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…
We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly…
In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural…
Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and…
A case-based reasoning (CBR) system solves a new problem by retrieving `cases' that are similar to the given problem. If such a system can achieve high accuracy, it is appealing owing to its simplicity, interpretability, and scalability. In…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians…
By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3-form C-field leads to deformations of the algebras of multi-vectors on the Dirichlet-brane world-volume as 2-algebras. This would shed some new…
Considering a probability distribution over parameters is known as an efficient strategy to learn a neural network with non-differentiable activation functions. We study the expectation of a probabilistic neural network as a predictor by…
The brain anticipates future events using internal models that specify not only what will occur, but also when it will occur and with what probability. We refer to this joint specification of identity, timing, and likelihood as a complete…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
The embedding space of language models is widely believed to capture the semantic relationships; for instance, embeddings of digits often exhibit an ordered structure that corresponds to their natural sequence. However, the mechanisms…
Let $\mathcal{P}_{\beta}^{(V)} (N_{\cal I})$ be the probability that a $N\times N$ $\beta$-ensemble of random matrices with confining potential $V(x)$ has $N_{\cal I}$ eigenvalues inside an interval ${\cal I}=[a,b]$ of the real line. We…
This paper develops some general calculus for GGC and Dirichlet process means functionals. It then proceeds via an investigation of positive Linnik random variables, and more generally random variables derived from compositions of a stable…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…