Related papers: Probabilistic Approach to Neural Networks Computat…
Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…
Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well…
We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
In this paper we propose a simple yet powerful method for learning representations in supervised learning scenarios where each original input datapoint is described by a set of vectors and their associated outputs may be given by soft…
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically,…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…
Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…