Maximization Of Expectation Research Articles

Multi-objective optimization of committee selection for hierarchical Byzantine fault tolerance-based consensus protocols

Decentralized platforms like blockchain have been attracting significant attention in recent years, especially in the context of financial and payment systems. They are designed to provide a transparent, secure, and reliable environment for digital transactions without the need for a central authority. The core of a decentralized platform like blockchain is a consensus layer that allows all participants (called Workers), who properly operate and follow all network protocols and have access to the same state of the distributed ledger, to coordinate their actions and arrive at the same decisions. However, some Workers may be temporarily offline at their own discretion, without any confirmation, or their work may be faulty due to technical circumstances, resulting in unpredictable behavior. The goal of this article is to present an approach for multi-objective optimizing of Byzantine fault tolerance (BFT)-based consensus protocols, to reduce the impact on the network of faulty participants. Two criteria were considered – minimization of the number of sent service messages, and maximization of the mathematical expectation of the number of produced blocks. The result is a method to determine the optimal committee size and distribution of Workers, depending on their total number in the network and the expected proportion of Byzantine faulty nodes. All protocol amendments presented in this work are tested with corresponding simulation models and have demonstrated notable enhancements in the performance of the system and decreased the load on network nodes. These improvements will be implemented to the consensus protocol Gozalandia on the Waterfall platform, enhancing its overall reliability, performance, and security. In addition, the presented optimizing algorithm can be applied to a wide range of consensus protocols in blockchains, where blocks must be signed by randomly selected committees to confirm their validity

Logarithmic Moments for Mixture of Symmetric Alpha Stable Modelling

Mixture of symmetric <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable (s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> s) models can be used to model impulsive data with heavy-tailed distribution. Lack of closed-form expression for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable distributions is a challenge for efficient mixture modeling in current methods. In this letter, we present an analytical approach for novel solution of parameter estimation in s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> s mixture models which improves the computational efficiency of the existing methods. In addition, by introducing a centro-symmetrization (CS) transform, we generalize the application of proposed method to non-centered skewed data as well. The proposed method employs the logarithmic moments of data in maximization of conditional expectation of log-likelihood and is called EMLM algorithm. The experimental results on the synthetic and real datasets show that EMLM outperforms current baseline models not only in terms of goodness of fit of model, but also by increasing the performance of down-stream applications such as classification.

EM‐based adaptive divided difference filter for nonlinear system with multiplicative parameter

SummaryThis paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E‐)step and Maximization (M‐)step to meet such requirement. Firstly, E‐step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade‐off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete‐data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M‐step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E‐step and M‐step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second‐order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM‐based adaptive version of divided difference filter to the unknown or time‐varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley &amp; Sons, Ltd.

How and why actions are selected: action selection and the dark room problem

Abstract In this paper, I examine an evolutionary approach to the action selection problem and illustrate how it helps raise an objection to the predictive processing account. Clark examines the predictive processing account as a theory of brain function that aims to unify perception, action, and cognition, but - despite this aim - fails to consider action selection overtly. He off ers an account of action control with the implication that minimizing prediction error is an imperative of living organisms because, according to the predictive processing account, action is employed to fulfill expectations and reduce prediction error. One way in which this can be achieved is by seeking out the least stimulating environment and staying there (Friston et al. 2012: 2). Bayesian, neuroscientific, and machine learning approaches into a single framework whose overarching principle is the minimization of surprise (or, equivalently, the maximization of expectation. But, most living organisms do not find, and stay in, surprise free environments. This paper explores this objection, also called the “dark room problem”, and examines Clark’s response to the problem. Finally, I recommend that if supplemented with an account of action selection, Clark’s account will avoid the dark room problem.

Real-Time Energy Imbalance Management Scheme for Electric Vehicles in the Smart Grid

Electric Vehicles (EVs) as the alternative of the current fossil fuels vehicles represent the most promising green approach to the electrification of a significant portion of the transportation sector. Taking the randomness of EV's charging/ discharging characteristics into consideration, a significant uncertainty will be added to the grid by the large penetration of EVs. Consequently, charging/ discharging management of EVs in presence of large scale intermittent Renewable Energy Resources (RERs) are considered as the most significant challenge for the future smart grid. In this context, a novel market-oriented energy imbalance management scheme is proposed for the seamless integration of EVs to the grid. The proposed scheme which, unlike previous works, utilizes the grid's operating characteristics model within the signaling game-theoretic approach for the successful operation of electicity market. Optimal decision strategies for both EV owners and utility are devised by capturing the conflicting economic interests of players together under load/generation uncertainities. The maximization of the profit expectation of each market player in the presence of independent multi-generation resources is considered. This facilitates both the customer and utility to derive their robust bidding strategies. The efficacy of the proposed approach in reducing peak loads while satisfying customers needs are demonstrated by simulating the various scenarios of different penetration levels of EVs to the grid. Results show that the proposed methodology can successfully alleviate the peaks caused by the mass adoption of EVs with the better utilization of RER.

A convergent non-negative deconvolution algorithm with Tikhonov regularization

The main contribution of this paper is to present a convergent and flexible deconvolution algorithm based on the well-known Tikhonov-regularized least squares estimate under non-negativity constraints. The key idea for developing the algorithm is to replace the minimization of the cost function at each iteration by the minimization of a surrogate function, leading to a guaranteed decrease in the cost function. The algorithm derivation can also be interpreted as the expectation maximization process, where the surrogate function may be viewed as the negative conditional expectation, and then the minimization of the surrogate function is equivalent to the maximization of the conditional expectation. The proposed algorithm has some favorable properties, including the monotonic decrease of the cost function, the self-constraining in the feasible region and the absence of a pre-determined step size. This algorithm can be seen as a special case of Lanteri's method, but this paper theoretically proves that the iteration sequence will converge to a global solution. The simulation results confirm similar behaviors of Lanteri's method and the proposed one. The results also demonstrate that the proposed algorithm provides a performance comparable to those of the other commonly used methods as regards restoration ability, convergence speed and computational cost.

Free-Energy Minimization and the Dark-Room Problem

Recent years have seen the emergence of an important new fundamental theory of brain function. This theory brings information-theoretic, Bayesian, neuroscientific, and machine learning approaches into a single framework whose overarching principle is the minimization of surprise (or, equivalently, the maximization of expectation). The most comprehensive such treatment is the “free-energy minimization” formulation due to Karl Friston (see e.g., Friston and Stephan, 2007; Friston, 2010a,b – see also Fiorillo, 2010; Thornton, 2010). A recurrent puzzle raised by critics of these models is that biological systems do not seem to avoid surprises. We do not simply seek a dark, unchanging chamber, and stay there. This is the “Dark-Room Problem.” Here, we describe the problem and further unpack the issues to which it speaks. Using the same format as the prolog of Eddington’s Space, Time, and Gravitation (Eddington, 1920) we present our discussion as a conversation between: an information theorist (Thornton), a physicist (Friston), and a philosopher (Clark).

A comparison of MAD and CVaR models with real features

In this paper we consider two different mixed integer linear programming models for solving the single period portfolio selection problem when integer stock units, transaction costs and a cardinality constraint are taken into account. The first model has been formulated by using the maximization of the worst conditional expectation as objective function. The second model is based on the maximization of the safety measure corresponding to the mean absolute deviation. Extensive computational results are provided to compare the financial characteristics of the optimal portfolios selected by the two models on real data from European stock exchange markets. Some simple heuristics are also introduced that provide efficient and effective solutions when an optimal integer solution cannot be found in a reasonable amount of time.

An Approach to Parameter Estimation and Stochastic Control in Water Resources With an Application to Reservoir Operation

This paper presents an algorithm for the estimation of parameters in state‐space models that represent hydrologic processes in which the state variables are observed with error. The algorithm is based on the maximization of the conditional expectation of the likelihood function of the state equation. The estimation algorithm is numerically stable and guarantees local convergence under mild conditions. It is also shown that the estimation algorithm can be coupled with an optimal control method to yield a combined control estimation technique that can be easily implemented. An application of the theory and methods developed herein is given for flood routing via reservoir operation.

Specification and Estimation of Cobb-Douglas Production Function Models

In this paper we consider the specification and estimation of the Cobb-Douglas production function model. After reviewing the specifying assumptions for the model which are based on deterministic profit maximization, we develop a model in which profits are stochastic and in which maximization of the mathematical expectation of profits is posited. Sampling and Bayesian estimation techniques for this model are presented. IN THIS PAPER we take up the problem of specifying and estimating a model of a profit maximizing firm operating with a Cobb-Douglas production function. Our model differs from the traditional production model considered in the literature, in that we assume that: (a) the production process is neither instantaneous nor deterministic; and (b) entrepreneurs are aware of the stochastic nature of production in their profit maximizing endeavors. This fundamental conceptual difference in our approach leads us to a new model with properties different from that of the traditional model.2 Also we develop both sampling theory and Bayesian estimation procedures for the new model. The order of presentation is as follows. In Section 2 we review the traditional model, and then go on in Section 3 to formulate the new model. In Section 4, sampling theory estimation procedures are developed for the new model. In contrast with the traditional model, it is found that classical least squares provides consistent estimators of the parameters of the Cobb-Douglas production function. With a normality assumption, these are also unbiased and maximum likelihood estimators. Finally, in Section 5, a Bayesian analysis of the new model is presented.