Exact Expectation Research Articles

An Exact Expectation Model for the LMS Tracking Abilities

Nonstationary environments are ubiquitous in communications and acoustic systems. The ability to track their dynamics is one of the most desirable features of adaptive processing algorithms. The designers of these algorithms employ guidelines derived from stochastic analyses to adjust user-defined parameters to maximize performance or avoid stability issues. It is therefore important that analyzes of adaptive processing algorithms take into account the built-in sophisticated learning capabilities. This work presents a comprehensive model of the performance of the least mean square algorithm, operating under Markovian time-varying channels. Our advanced analysis considers both transient and steady-state regimes. Furthermore, in our analysis, the popular independence assumption is not adopted, resulting in a stochastic model which is accurate even when: (i) the step size is not infinitesimally small; or (ii) when the unknown system presents a high nonstationary degree. In addition, our evaluation is also able to provide a deterministic theoretical step-size sequence that optimizes algorithmic performance, as well as an accurate step size upper bound that guarantees algorithm stability. Computer simulations performed are in accordance with our theoretical predictions.

Exact expectation analysis of the LMS adaptive identification of non‐linear systems

Most adaptive filtering schemes employ the tapped-delay line. In part, such a fact can be explained by the assumption that the plant they intend to estimate is linear. Although such a hypothesis can be reasonable if the input signal is constrained to a certain range, sometimes it may not be valid. In this last case, the performance and stability guarantees provided by stochastic models that presume linearity of the ideal system are no longer valid. This Letter advances an analytic model of the least-mean-square (LMS) learning capabilities when the ideal system is not linear, with the additive noise including non-linear functions of the input samples. The proposed analysis does not assume neither that the excitation signal is statistically independent of the adaptive weights, nor that the additive noise is white and/or independent of input data. Furthermore, it can be applied to non-Gaussian and/or non-white input signals. Simulations show that the advanced model is more accurate than traditional approaches.

Dynamical generation of quark/lepton mass hierarchy in an extra dimension

Abstract We show that the observed quark/lepton mass hierarchy can be realized dynamically on an interval extra dimension with point interactions. In our model, the positions of the point interactions play a crucial role in controlling the quark/lepton mass hierarchy and are determined by the minimization of the Casimir energy. By use of the exact extra-dimensional coordinate-dependent vacuum expectation value of a gauge-singlet scalar, we find that there is a parameter set, where the positions of the point interactions are stabilized and fixed, which can reproduce the experimental values of the quark masses precisely enough, while the charged lepton part is less relevant. We also show that possible mixings among the charged leptons will improve the situation significantly.

Combined Belief Propagation-Mean Field Message Passing Algorithm for Dirichlet Process Mixtures

This letter deals with variational inference for Dirichlet process mixtures (DPM) models. We propose a combined message-passing algorithm introducing belief propagation (BP) into the original mean field (MF) rules, which leads to a more precise approximate posterior in DPM. To compute the BP message, we change an exponential distribution to a non-exponential utilizing a flexible expression of Dirac delta function. Therefore, BP rules can be used to handle such functions, resulting to a local exact expectation instead of approximate expectation from the original MF method. Simulation results show that the proposed combined BP-MF algorithm results in a significant performance improvement compared to the state-of-the-art inference methods.

Weather Forecasting Pridiction using Mamdani Fuzzifier

A climate expectation display is under study in view of the neural system and fuzzy surmising framework, and after that apply it to anticipate every day fuzzy precipitation given meteorological premises for testing. A "fuzzy ranked based neural system", which reenacts successive relations among fuzzy sets utilizing the manufactured neural system. It is outstanding that the requirement for exact climate expectation is clear while thinking about the advantages. Nonetheless, the over the top quest for exactness in climate expectation makes a portion of the "precise" forecast comes about pointless and the numerical forecast show is regularly intricate and tedious.

On Nodes of Small Degrees and Degree Profile in Preferential Dynamic Attachment Circuits

We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree $0$ (terminal nodes) and outdegree $1$ in a very large circuit. The expectation and variance of the number of those two types of nodes are both asymptotically linear with respect to the age of the circuit. We show that the numbers of nodes of outdegree $0$ and $1$ asymptotically follow a two-dimensional Gaussian law via multivariate martingale methods. We also study the exact distribution of the degree of a node, as the circuit ages, via a series of P\'olya-Eggenberger urn models with "hiccups" in between. The exact expectation and variance of the degree of nodes are determined by recurrence methods. Phase transitions of these degrees are discussed briefly. This is an extension of the abstract [20].

Exact expectation analysis of the deficient-length LMS algorithm

Stochastic models that predict adaptive filtering algorithms performance usually employ several assumptions in order to simplify the analysis. Although these simplifications facilitate the recursive update of the statistical quantities of interest, they by themselves may hamper the modeling accuracy. This paper simultaneously avoids for the first time the employment of two ubiquitous assumptions often adopted in the analysis of the least mean squares (LMS) algorithm. The first of them is the so-called independence assumption, which presumes statistical independence between adaptive coefficients and input data. The second one assumes a sufficient-order configuration, in which the lengths of the unknown plant and the adaptive filter are equal. State equations that characterize both the mean and mean square performance of the deficient-length configuration without using the independence assumption are provided. The devised analysis, encompassing both transient and steady-state regimes, is not restricted neither to white nor to Gaussian input signals and is able to provide a proper step size upper bound that guarantees stability.

Exact analysis of the least‐mean‐square algorithm with coloured measurement noise

In general, theoretical analyses of adaptive filtering algorithms employ statistical approximations in order to render the derivations tractable. Among such hypotheses, the statistical independence between the current adaptive coefficients and past input vectors is a very popular one. Unfortunately, this simplification gives rise to discrepancies with respect to empirical results, especially for large values of the step-size parameter. In this Letter, this issue is overcome by the usage of an exact expectation analysis (i.e. a stochastic model that does not employ the above-mentioned independence assumption) of the least-mean-squares adaptive algorithm. The authors analysis is also generalised in order to address the common case of coloured additive noise, an issue that is so far missing from the literature. The accuracy of the advanced model is verified through simulations.

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

This paper addresses the non-fragile control problem for a class of uncertain linear systems subject to model uncertainty, controller perturbations, fault signals and input constraints. The controller to be designed is supposed to have additive gain perturbations. A novel state feedback controller is proposed based on the exact available expectation of a Bernoulli random variable, which is introduced to model the feature of the controller gain perturbation that randomly occurs. By using Lyapunov stability theory, new sufficient conditions are derived to design non-fragile controller for a class of uncertain linear systems considering input constraints. Compared with the existing non-fragile state feedback controller methods, the non-fragile property is fully considered to improve the tolerance of uncertainties in the controller, where the conservativeness can be reduced via the Bernoulli random variable. The effectiveness of the proposed control strategy is illustrated by two numerical examples.

Exact finite volume expectation values of overline{varPsi}varPsi in the massive Thirring model from light-cone lattice correlators

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator overline{varPsi}varPsi between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator overline{varPsi}varPsi is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

A note on the expected value of the Rand index.

Two expectations of the adjusted Rand index (ARI) are compared. It is shown that the expectation derived by Morey and Agresti (1984, Educational and Psychological Measurement, 44, 33) under the multinomial distribution to approximate the exact expectation from the hypergeometric distribution (Hubert & Arabie, 1985, Journal of Classification, 2, 193) provides a poor approximation, and, in some cases, the difference between the two expectations can increase with the sample size. Proofs concerning the minimum and maximum difference between the two expectations are provided, and it is shown through simulation that the ARI can differ significantly depending on which expectation is used. Furthermore, when compared in a hypothesis testing framework, multinomial approximation overly favours the null hypothesis.

Supersymmetric R\xe9nyi entropy and defect operators

We describe the defect operator interpretation of the supersymmetric Rényi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary {mathbb{Z}}_n gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Rényi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects.

ANALYSIS OF RATING PREDICTION SYSTEM FROM TEXTUAL REVIEWS

In this work, we propose a slant based rating forecast technique to enhance expectation exactness in recommender frameworks. Right off the bat, it proposes a social client nostalgic estimation approach and computes every client's supposition on things. Furthermore, it considers a client's own wistful traits, as well as think about relational nostalgic impact. At that point, consider thing notoriety, which can be induced by the wistful conveyances of a client set that mirror clients' thorough assessment. Finally, by combining three variables client notion closeness, relational wistful impact, and thing's notoriety comparability into a recommender Framework to make an exact rating expectation. It leads an execution assessment of the three wistful components on a genuine informational index.

Smoothing the payoff for efficient computation of Basket option prices

We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.

Extending the Cascaded Gaussian Mixture Regression Framework for Cross-Speaker Acoustic-Articulatory Mapping

This paper addresses the adaptation of an acoustic-articulatory inversion model of a reference speaker to the voice of another source speaker, using a limited amount of audio-only data. In this study, the articulatory-acoustic relationship of the reference speaker is modeled by a Gaussian mixture model and inference of articulatory data from acoustic data is made by the associated Gaussian mixture regression (GMR). To address speaker adaptation, we previously proposed a general framework called Cascaded-GMR (C-GMR) which decomposes the adaptation process into two consecutive steps: spectral conversion between source and reference speaker and acoustic-articulatory inversion of converted spectral trajectories. In particular, we proposed the integrated C-GMR technique (IC-GMR) in which both steps are tied together in the same probabilistic model. In this paper, we extend the C-GMR framework with another model called Joint-GMR (J-GMR). Contrary to the IC-GMR, this model aims at exploiting all potential acoustic-articulatory relationships, including those between the source speaker's acoustics and the reference speaker's articulation. We present the full derivation of the exact expectation–maximization (EM) training algorithm for the J-GMR. It exploits the missing data methodology of machine learning to deal with limited adaptation data. We provide an extensive evaluation of the J-GMR on both synthetic acoustic-articulatory data and on the multispeaker MOCHA EMA database. We compare the J-GMR performance to other models of the C-GMR framework, notably the IC-GMR, and discuss their respective merits.

Baum–Welch algorithm on directed acyclic graph for mixtures with latent Bayesian networks

We consider a mixture model with latent Bayesian network (MLBN) for a set of random vectors . Each X(t) is associated with a latent state st, given which X(t) is conditionally independent from other variables. The joint distribution of the states is governed by a Bayes net. Although specific types of MLBN have been used in diverse areas such as biomedical research and image analysis, the exact expectation–maximization (EM) algorithm for estimating the models can involve visiting all the combinations of states, yielding exponential complexity in the network size. A prominent exception is the Baum–Welch algorithm for the hidden Markov model, where the underlying graph topology is a chain. We hereby develop a new Baum–Welch algorithm on directed acyclic graph (BW‐DAG) for the general MLBN and prove that it is an exact EM algorithm. BW‐DAG provides insight on the achievable complexity of EM. For a tree graph, the complexity of BW‐DAG is much lower than that of the brute‐force EM. Copyright © 2017 John Wiley & Sons, Ltd.

Non-equilibrium current cumulants and moments with a point-like defect

We derive the exact n-point current expectation values in the Landauer–Büttiker non-equilibrium steady state of a multi terminal system with star graph geometry and a point-like defect localised in the vertex. The current cumulants are extracted from the connected correlation functions and the cumulant generating function is established. We determine the moments, show that the associated moment problem has a unique solution and reconstruct explicitly the corresponding probability distribution. The basic building blocks of this distribution are the probabilities of particle emission and absorption from the heat reservoirs, driving the system away from equilibrium. We derive and analyse in detail these probabilities, showing that they fully describe the quantum transport problem in the system.

Empirical Dynamic Programming

We propose empirical dynamic programming algorithms for Markov decision processes. In these algorithms, the exact expectation in the Bellman operator in classical value iteration is replaced by an empirical estimate to get “empirical value iteration” (EVI). Policy evaluation and policy improvement in classical policy iteration are also replaced by simulation to get “empirical policy iteration” (EPI). Thus, these empirical dynamic programming algorithms involve iteration of a random operator, the empirical Bellman operator. We introduce notions of probabilistic fixed points for such random monotone operators. We develop a stochastic dominance framework for convergence analysis of such operators. We then use this to give sample complexity bounds for both EVI and EPI. We then provide various variations and extensions to asynchronous empirical dynamic programming, the minimax empirical dynamic program, and show how this can also be used to solve the dynamic newsvendor problem. Preliminary experimental results suggest a faster rate of convergence than stochastic approximation algorithms.

Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory

We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

Mirror symmetry and loop operators

Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.