Related papers: Probabilistic Approach to Neural Networks Computat…
We analyze algorithmic and computational aspects of biological phenomena, such as replication and programmed death, in the context of machine learning. We use two different measures of neuron efficiency to develop machine learning…
Most of the fundamental, emergent, and phenomenological parameters of particle and nuclear physics are determined through parametric template fits. Simulations are used to populate histograms which are then matched to data. This approach is…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of…
Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in…
In this work we derive Born's rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to a environement made of "qubits" (i.e., Bohmian pointers) we show that entanglement together with…
Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
We introduce a two state vector formalism of quantum mechanics by generalizing Bell hidden variable model to higher dimensions and by attributing a physical significance, a state evolving backward in time, to the hidden variable. A simple…
Probabilistic Circuits (PCs) are prominent tractable probabilistic models, allowing for a range of exact inferences. This paper focuses on the main algorithm for training PCs, LearnSPN, a gold standard due to its efficiency, performance,…
In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods.…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
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,…
QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. The fundamental gambit is to represent states and measurements, as well as time…