Improving the training time of support vector regression algorithms through novel hyper-parameters search space reductions

The selection of hyper-parameters in support vector machines (SVM) is a key point in the training process of these models when applied to regression problems. Unfortunately, an exact method to obtain the optimal set of SVM hyper-parameters is unknown, and search algorithms are usually applied to obtain the best possible set of hyper-parameters. In general these search algorithms are implemented as grid searches, which are time consuming, so the computational cost of the SVM training process increases considerably. This paper presents a novel study of the effect of including reductions in the range of SVM hyper-parameters, in order to reduce the SVM training time, but with the minimum possible impact in its performance. The paper presents reduction in parameter C, by considering its relation with the rest of SVM hyper-parameters (γ and ε), through an approximation of the SVM model. On the other hand, we use some characteristics of the Gaussian kernel function and a previous result in the literature to obtain novel bounds for γ and ε hyper-parameters. The search space reductions proposed are evaluated in different regression problems from UCI and StatLib databases. All the experiments carried out applying the popular LIBSVM solver have shown that our approach reduces the SVM training time, maintaining the SVM performance similar to when the complete range in SVM parameters is considered.     

P-selective sets,tally languages,and the behavior of polynomial time reducibilities onNP

The notion ofp-selective sets, and tally languages, are used to study polynomial time reducibilities onNP. P-selectivity has the property that a setA belongs to the classP if and only if both _m ^p A andA isp-selective. We prove that for every tally language set inNP there exists a polynomial time equivalent set inNP that isp-selective. From this result it follows that if NEXT DEXT, then polynomial time Turing and many-one reducibilities differ onNP. This research was supported in part by the National Science Foundation under grant MCS 77-23493     

Calculational derivation of a counter with bounded response time and bounded power dissipation

Summary A counter is calculationally designed by applying a functional way of programming, in which a machine is conceived as a function from states to behaviours. The design exploits the fine-grained concurrency available in VLSI. It is obtained by applying a series of correctness-preserving transformations on an initial design, which satisfies the functional specification but does not meet the cost/performance requirements. The transformations are purely calculational, i.e. they are based on a few simple axioms. The design is generic in that it describes counters with all possible periods. An attractive property of the design is that all these counters have the same response time as well as the same power dissipation. Joep Kessels is a senior scientist at Philips Research Laboratories. He was involved in projects on applicative programming, distributed processing and local area networks. Currently he is engaged in a project on designing asynchronous VLSI circuits. His main research interests are design methodology and distributed processing.     

The application of ridge polynomial neural network to multi-step ahead financial time series prediction

Motivated by the slow learning properties of multilayer perceptrons (MLPs) which utilize computationally intensive training algorithms, such as the backpropagation learning algorithm, and can get trapped in local minima, this work deals with ridge polynomial neural networks (RPNN), which maintain fast learning properties and powerful mapping capabilities of single layer high order neural networks. The RPNN is constructed from a number of increasing orders of Pi–Sigma units, which are used to capture the underlying patterns in financial time series signals and to predict future trends in the financial market. In particular, this paper systematically investigates a method of pre-processing the financial signals in order to reduce the influence of their trends. The performance of the networks is benchmarked against the performance of MLPs, functional link neural networks (FLNN), and Pi–Sigma neural networks (PSNN). Simulation results clearly demonstrate that RPNNs generate higher profit returns with fast convergence on various noisy financial signals.     

A very simple function that requires exponential size nondeterministic graph-driven read-once branching programs

Branching programs are a well-established computation model for Boolean functions, especially read-once branching programs (BP1s) have been studied intensively. A very simple function f in n² variables is exhibited such that both the function f and its negation ¬f can be computed by Σ³_p-circuits, the function f has nondeterministic BP1s (with one nondeterministic node) of linear size and ¬f has size O(n⁴) for oblivious nondeterministic BP1s but f requires nondeterministic graph-driven BP1s of size . This answers an open question stated by Jukna, Razborov, Savický, and Wegener [Comput. Complexity 8 (1999) 357-370].     

Comments on ‘nonlinear H∞ output feedback control with integrator for polynomial discrete‐time systems’

This note points out that controllers resulting from Corollaries 3.1 and 3.2 and Theorem 3.1 in Saat and Nguang (Int. J. Robust Nonlinear Control 2013; 10.1002/rnc.3130) do not improve over the open‐loop performance. Copyright © 2014 John Wiley & Sons, Ltd.     

The problem of guaranteeing the absence of a complete set of reductions

This article is the twelfth of a series of articles discussing various open research problems in automated reasoning. Here we focus on finding criteria for guaranteeing the absence of a complete set of reductions. We include a suggestion for evaluating a proposed solution to this research problem.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

拟合实验数据的新方程--非整数幂多项式方程

将实验数据拟合成方程在科学研究和工程计算上具有十分重要的作用。目前,拟合实验数据最常用的是整数幂多项式f(x)=c0 c1x c2x^2… cnx^n但是用此多项式拟合各类数据时有时误差较大。本文提出一个新方程,即双系列非整数幂多项式g(x)=c0 c1x^a…… ckx^ka ck 1x^(k 1)b ……cnx^nb式中a,b为参数ci(i=0,1,2,3,……n)为待定系数。在拟合各类实验数据时,新方程总是优于整数幂多项式。     

The problem of determining the size of a complete set of reductions

This article is the tenth of a series of articles discussing various open research problems in automated reasoning. Here we focus on finding criteria for accurately predicting the size of a complete set of reductions when such a set exists. We include a suggestion for evaluating a proposed solution to this research problem.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

The Branching-Time Transformation Technique for Chain Datalog Programs

The branching-time transformation technique has proven to be an efficient approach for implementing functional programming languages. In this paper we demonstrate that such a technique can also be defined for logic programming languages. More specifically, we first introduce Branching Datalog, a language that can be considered as the basis for branching-temporal deductive databases. We then present a transformation algorithm from Chain Datalog programs to the class of unary Branching Datalog programs with at most one IDB atom in the body of each clause. In this way, we obtain a novel implementation approach for Chain Datalog, shedding at the same time new light on the power of branching-time logic programming.     

The problem of guaranteeing the existence of a complete set of reductions

This article is the eleventh of a series of articles discussing various open research problems in automated reasoning. Here we focus on finding criteria for guaranteeing the existence of a complete set of reductions. We include a suggestion for evaluating a proposed solution to this research problem.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

The best polynomial multidimensional-matrix regression

The problem of finding the best polynomial multidimensional-matrix regression is formulated. A system of equations is obtained to calculate the parameters of polynomial regression of any degree. Expressions for the parameters of constant linear and square regressions are derived as well. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 138–143, May–June 2007.     

Symmetry reductions for model checking of concurrent dynamic software

Symmetry reduction techniques exploit symmetries that occur during the execution of a system in order to minimize its state space for efficient verification of temporal logic properties. This paper presents a framework for concisely defining and evaluating symmetry reductions currently used in software model checking, involving heap objects and processes. An on-the-fly state space exploration algorithm combining both techniques will also be presented. Second, the relation between symmetry and partial-order reductions is investigated, showing how ones strengths can be used to compensate for the others weaknesses. The symmetry reductions presented here were implemented in the dSPIN model-checking tool. We also performed a number of experiments that show significant progress in reducing the cost of finite-state software verification.     

Financial time series prediction using polynomial pipelined neural networks

This paper proposes a novel type of higher-order pipelined neural network: the polynomial pipelined neural network. The proposed network is constructed from a number of higher-order neural networks concatenated with each other to predict highly nonlinear and nonstationary signals based on the engineering concept of divide and conquer. The polynomial pipelined neural network is used to predict the exchange rate between the US dollar and three other currencies. In this application, two sets of experiments are carried out. In the first set, the input data are pre-processed between 0 and 1 and passed to the neural networks as nonstationary data. In the second set of experiments, the nonstationary input signals are transformed into one step relative increase in price. The network demonstrates more accurate forecasting and an improvement in the signal to noise ratio over a number of benchmarked neural networks.     

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.     

Wronskian-based tests for stability of polynomial combinations

In this paper, a stability criterion based on counting the real roots of two specific polynomials is formulated. To establish this result, it is shown that a hyperbolicity condition and a strict positivity of a polynomial Wronskian are necessary and sufficient for the stability of any real polynomial. This result is extended to the stability study of some linear combinations of polynomials. Necessary and sufficient conditions of stability are obtained for polynomial segments and planes.     

BPP and the polynomial hierarchy

BPP is the class of all sets that can be divided by a probabilistic Turing machine with bounded error probability within a polynomial time bound. Sipser (1983) showed that BPP is contained in the polynomial hierarchy of Meyer and Stockmeyer.In this paper it is shown by pure counting arguments that BPP is contained in Σ^P₂, the second level of the hierarchy.     

Potentials of GHG reductions from wastewater treatment for the CDM

The study aims to evaluate the potential of GHG (greenhouse gas) reductions by installing an anaerobic digester in a wastewater treatment facility in Southeast Asia. Then the break-even point of additional investment to reduce GHG is obtained by exchanging carbon price as emissions credits. In the project scenario, the wastewater treatment system has the digester, where methane (biogas) is produced and recovered. Compared with the baseline scenario, the biogas has calorific value to produce heat and electri...