Recently, it has been shown that a probabilistic model based on two of the main concepts in quantum physics - a density matrix and the Born rule, can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework. It has been shown that the proposed probabilistic interpretation is suitable for modeling on-line learning algorithms for Independent /Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point detection. Here, it will be shown that the proposed model can be successfully used in other areas of applied signal processing, with some examples of applications in the area of power electronics and general classification problems.
Recently, it has been shown that a probabilistic model based on two of the main concepts in quantum physics - a density matrix and the Born rule, can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework. It has been shown that the proposed probabilistic interpretation is suitable for modeling on-line learning algorithms for Independent /Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point detection. Here, it will be shown that the proposed model can be successfully used in other areas of applied signal processing, with some examples of applications in the area of power electronics and general classification problems.
Recently, the several applications of the probabilistic model based on two of the main concepts in quantum physics - a density matrix and the Born rule, have been introduced. It was shown that the model can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework, like it is the case of on-line learning algorithms for Independent /Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point detection, with some examples of applications in the area of power electronics and general classification problems. Here, we present a robust on-line Principal Component Algorithm based on the proposed model, which extracts several principal components simultaneously. Also, we will show usefulness of the proposed method in a simple example of image segmentation.
In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework. Model is based on two of the main concepts in quantum physics - a density matrix and the Born rule. As an example, we will show that proposed probabilistic interpretation is suitable for modeling of on-line learning algorithms for PSA, which are preferably realized by a parallel hardware based on very simple computational units. Proposed concept (model) can be used in the context of improving algorithm convergence speed, learning factor choice, or input signal scale robustness. We are going to see how the Born rule and the Hebbian learning rule are connected
It is well known that the field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories. There are many algorithms based on different theoretical backgrounds that could be used for pattern recognition in practical applications. Generally, most of the algorithms are applied in areas like classification, regression or change point detection.Recently, it has been shown that a probabilistic model based on two of the main concepts in quantum physics – a density matrix and the Born rule, can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework. It has been shown that the proposed probabilistic interpretation is suitable for modeling on-line learning algorithms for Independent/Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point or anomalies detection as well as simple classification problems. Here another application of the proposed quantum probabilistic model is going to be presented. A general paradigm called QLEAR learning (Quantum Low Entropy based Associative Reasoning) would be presented and tested in classification context. Proposed method potentially can overcome the problem that classifier performance depends greatly on the characteristics of the data to be classified. It is known that until now, there is no single classifier that works best on all given problems (a phenomenon that may be explained by the no-free-lunch theorem). Here we will try to propose a classification algorithm that, actually, automatically adjusts its performance according to characteristics of the data on which it is applied. An interesting aspect is that proposed method inherently solves the problem of unbalanced classes (classes that have significantly different size). The proposed paradigm can be applied in any area in which standard classification techniques are applied. The method is going to be analyzed in the context of classification, prediction and solving some mathematical problems.We’ll analyze, mainly, the case in which data is represented by vectors. Generalization toward multiway data would be discussed only on one example. The approach is based on the idea that classification can be understood as supervised clustering, where quantum entropy, in the context of the quantum probabilistic model, will be used as a “capturer” (measure, or external index) of the “natural structure” of the data. By using quantum entropy we don’t make any assumption about linear separability of the data that are going to be classified. The basic idea is to find close neighbours to a query sample and then use relative change in the quantum entropy as a measure of similarity of the newly arrived sample with the representatives of interest. In other words, method is based on calculation of quantum entropy of the referent system and its relative change with the addition of the newly arrived sample. Referent system consists of vectors/matrices that represent individual classes and that are the most similar, in Euclidean distance sense, to the vector that is analyzed. The classification problem is analysed in the context of measuring similarities to prototype examples of categories. The proposed method could be seen as a hybrid of nearest neighbor and optimization machine learning technique which deals naturally with the multiclass setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice.
The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.
Despite the many challenges in exploratory data analysis, artificial neural networks have motivated strong interests in scientists and researchers both in theoretical as well as practical applications. Among sources of such popularity of artificial neural networks the ability of modeling non-linear dynamical systems, generalization, and adaptation possibilities should be mentioned. Despite this, there is still significant debate about the role of various underlying stochastic processes in stabilizing a unique structure for data learning and prediction. One of such obstacles to the theoretical and numerical study of machine intelligent systems is the curse of dimensionality and the sampling from high-dimensional probability distributions. In general, this curse prevents efficient description of states, providing a significant complexity barrier for the system to be efficiently described and studied. In this strand of research, direct treatment and description of such abstract notions of learning theory in terms of quantum information be one of the most favorable candidates. Hence, the subject matter of these articles is devoted to problems of design, adaptation and the formulations of computationally hard problems in terms of quantum mechanical systems. In order to characterize the microscopic description of such dynamics in the language of inferential statistics, covariance matrix estimation of d-dimensional Gaussian densities and Bayesian interpretation of eigenvalue problem for dynamical systems is assessed.
Abstract : The broad term goal of this research program was to build a foundation for constructing probabilistic-dynamic systems from principles based on quantum as opposed to classical probability theory. So far we have applied these principles to both traditional, one-stage decision problems studied by decision researchers as well as dynamic Markov decision problems used in computer science and engineering. The more specific goal of the proposed research was to develop new applications of quantum probability applied to dynamic decision situations: (a) To develop a quantum reinforcement learning model for learning a sequence of actions in a Markov decision problem environments that is fast learning and robust with respect to changes in the environment; (b) To theoretically derive the convergence and speed of convergence properties of the new quantum learning algorithm for the dynamic environments; and most importantly, (c) To experimentally test whether the quantum reinforcement learning model provides a better account of actual human performance in Markov de