Bayesian network approach to multinomial parameter learning using data and expert judgments

One of the hardest challenges in building a realistic Bayesian Network (BN) model is to construct the node probability tables (NPTs). Even with a fixed predefined model structure and very large amounts of relevant data, machine learning methods do not consistently achieve great accuracy compared to the ground truth when learning the NPT entries (parameters). Hence, it is widely believed that incorporating expert judgments can improve the learning process. We present a multinomial parameter learning method, which can easily incorporate both expert judgments and data during the parameter learning process. This method uses an auxiliary BN model to learn the parameters of a given BN. The auxiliary BN contains continuous variables and the parameter estimation amounts to updating these variables using an iterative discretization technique. The expert judgments are provided in the form of constraints on parameters divided into two categories: linear inequality constraints and approximate equality constraints. The method is evaluated with experiments based on a number of well-known sample BN models (such as Asia, Alarm and Hailfinder) as well as a real-world software defects prediction BN model. Empirically, the new method achieves much greater learning accuracy (compared to both state-of-the-art machine learning techniques and directly competing methods) with much less data. For example, in the software defects BN for a sample size of 20 (which would be considered difficult to collect in practice) when a small number of real expert constraints are provided, our method achieves a level of accuracy in parameter estimation that can only be matched by other methods with much larger sample sizes (320 samples required for the standard machine learning method, and 105 for the directly competing method with constraints).     

Learning agents for the multi-mode project scheduling problem

Intelligent optimization refers to the promising technique of integrating learning mechanisms into (meta-)heuristic search. In this paper, we use multi-agent reinforcement learning for building high-quality solutions for the multi-mode resource-constrained project scheduling problem (MRCPSP). We use a network of distributed reinforcement learning agents that cooperate to jointly learn a well-performing constructive heuristic. Each agent, being responsible for one activity, uses two simple learning devices, called learning automata, that learn to select a successor activity order and a mode, respectively. By coupling the reward signals for both learning tasks, we can clearly show the advantage of using reinforcement learning in search. We present some comparative results, to show that our method can compete with the best performing algorithms for the MRCPSP, yet using only simple learning schemes without the burden of complex fine-tuning.     

Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries

Cross-national research studies such as the Program for International Student Assessment and the Third International Mathematics and Science Study (TIMSS) have contributed much to our understandings regarding country differences in student achievement in mathematics, especially at the primary (elementary) and lower secondary (middle school) levels. TIMSS, especially, has demonstrated the central role that the concept of opportunity to learn plays in understanding cross-national differences in achievement Schmidt et al., (Why schools matter: A cross-national comparison of curriculum and learning  2001). The curricular expectations of a nation and the actual content exposure that is delivered to students by teachers were found to be among the most salient features of schooling related to academic performance. The other feature that emerges in these studies is the importance of the teacher. The professional competence of the teacher which includes substantive knowledge regarding formal mathematics, mathematics pedagogy and general pedagogy is suggested as being significant—not just in understanding cross-national differences but also in other studies as well (Hill et al. in Am Educ Res J 42(2):371–406, 2005). Mathematics Teaching in the 21st Century (MT21) is a small, six-country study that collected data on future lower secondary teachers in their last year of preparation. One of the findings noted in the first report of that study was that the opportunities future teachers experienced as part of their formal education varied across the six countries (Schmidt et al. in The preparation gap: Teacher education for middle school mathematics in six countries, 2007). This variation in opportunity to learn (OTL) existed in course work related to formal mathematics, mathematics pedagogy and general pedagogy. It appears from these initial results that OTL not only is important in understanding K-12 student learning but it is also likely important in understanding the knowledge base of the teachers who teach them which then has the potential to influence student learning as well. This study using the same MT21 data examines in greater detail the configuration of the educational opportunities future teachers had during their teacher education in some 34 institutions across the six countries.     

Mathematics curriculum: a vehicle for school improvement

Different forms of curriculum determine what is taught and learned in US classrooms and have been used to stimulate school improvement and to hold school systems accountable for progress. For example, the intended curriculum reflected in standards or learning expectations increasingly influences how instructional time is spent in classrooms. Curriculum materials such as textbooks, instructional units, and computer software constitute the textbook curriculum, which continues to play a dominant role in teachers’ instructional decisions. These decisions influence the actual implemented curriculum in classrooms. Various curriculum policies, including mandated end-of-course assessments (the assessed curriculum) and requirements for all students to complete particular courses (e.g., year-long courses in algebra, geometry, and advanced algebra or equivalent integrated mathematics courses) are also being implemented in increasing numbers of states. The wide variation across states in their intended curriculum documents and requirements has led to a historic and precedent-setting effort by the Council of Chief State School Officers and the National Governors Association Council for Best Practices to assist states in the development and adoption of common College and Career Readiness Standards for Mathematics. Also under development by this coalition is a set of common core state mathematics standards for grades K-12. These sets of standards, together with advances in information technologies, may have a significant influence on the textbook curriculum, the implemented curriculum, and the assessed curriculum in US classrooms in the near future.     

Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect

This paper considers identical parallel-machine scheduling problem with past-sequence-dependent (psd) delivery times and learning effect. In electronic manufacturing industry, an electronic component may be exposed to certain electromagnetic field and requires an extra time for eliminating adverse effect after the main processing. The extra time is modeled as past-sequence-dependent delivery time in the literature, which is proportional to the waiting time in the system. It is also observed that the learning process reflects a decrease in the processing time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. In practice, one often has to deal with the scheduling problems with psd delivery times and learning effect. Identical parallel-machine setting is considered because the occurrence of resources in parallel is common in the real world. In this paper, three objectives are the minimization of the total absolute deviation of job completion times, the total load on all machines and the total completion time. We develop polynomial algorithms to optimally solve these problems.     

Gated Bayesian networks for algorithmic trading

This paper introduces a new probabilistic graphical model called gated Bayesian network (GBN). This model evolved from the need to represent processes that include several distinct phases. In essence, a GBN is a model that combines several Bayesian networks (BNs) in such a manner that they may be active or inactive during queries to the model. We use objects called gates to combine BNs, and to activate and deactivate them when predefined logical statements are satisfied. In this paper we also present an algorithm for semi-automatic learning of GBNs. We use the algorithm to learn GBNs that output buy and sell decisions for use in algorithmic trading systems. We show how the learnt GBNs can substantially lower risk towards invested capital, while they at the same time generate similar or better rewards, compared to the benchmark investment strategy buy-and-hold. We also explore some differences and similarities between GBNs and other related formalisms.     

Temporal Taylor’s scaling of facial electromyography and electrodermal activity in the course of emotional stimulation

High frequency psychophysiological data create a challenge for quantitative modeling based on Big Data tools since they reflect the complexity of processes taking place in human body and its responses to external events. Here we present studies of fluctuations in facial electromyography (fEMG) and electrodermal activity (EDA) massive time series and changes of such signals in the course of emotional stimulation. Zygomaticus major (ZYG; “smiling” muscle) activity, corrugator supercilii (COR; “frowning” muscle) activity, and phasic skin conductance (PHSC; sweating) levels of 65 participants were recorded during experiments that involved exposure to emotional stimuli (i.e., IAPS images, reading and writing messages on an artificial online discussion board). Temporal Taylor’s fluctuations scaling were found when signals for various participants and during various types of emotional events were compared. Values of scaling exponents were close to one, suggesting an external origin of system dynamics and/or strong interactions between system’s basic elements (e.g., muscle fibres). Our statistical analysis shows that the scaling exponents enable identification of high valence and arousal levels in ZYG and COR signals.     

Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation

The generalized multiquadric radial basis function (φ_j=[(x-x_j)²+c²]^β) has the exponent β and shape parameter c that play an important role in the accuracy of the approximation. In this study, we present a trigonometric variable shape parameter and exponent strategy and apply it to function interpolations and linear boundary value problems. Several numerical experiments with the uniformly spaced nodes show that the inverse multiquadric radial basis function (β = −0.5) with the trigonometric variable shape parameter c strategy results in the best accuracy for the one-dimensional interpolations; the trigonometric variable shape parameters and exponent strategy produces the best accuracy for the two-dimensional interpolations and linear boundary value problems. For the non-uniformly spaced nodes, the random variable shape parameter c and exponent β strategy produces the best accuracy for the two-dimensional boundary value problem.     

The quality of non-textual elements in mathematics textbooks: an exploratory comparison between South Korea and the United States

As an exploratory investigation, this study aims to analyze non-textual elements in some Korean and US mathematics textbooks using a conceptual framework whose components include accuracy, connectivity, contextuality, and conciseness. By analyzing three US textbooks and three Korean ones, the study not only shows patterns in the use of non-textual elements in mathematics textbooks in different contexts but also provides insights into how to assess the quality of non-textual elements in mathematics textbooks, which I hope will contribute to the provision of more meaningful and productive learning opportunities to school children. Overall, the results from this study show that there is significant difference across topics and textbooks, which implies different opportunities to learn through non-textual elements. This study makes a unique contribution to the conceptualization of non-textual elements in mathematics education and has implications for textbook analysis and curriculum development.     

Cross-validated bagged learning

Many applications aim to learn a high dimensional parameter of a data generating distribution based on a sample of independent and identically distributed observations. For example, the goal might be to estimate the conditional mean of an outcome given a list of input variables. In this prediction context, bootstrap aggregating (bagging) has been introduced as a method to reduce the variance of a given estimator at little cost to bias. Bagging involves applying an estimator to multiple bootstrap samples and averaging the result across bootstrap samples. In order to address the curse of dimensionality, a common practice has been to apply bagging to estimators which themselves use cross-validation, thereby using cross-validation within a bootstrap sample to select fine-tuning parameters trading off bias and variance of the bootstrap sample-specific candidate estimators. In this article we point out that in order to achieve the correct bias variance trade-off for the parameter of interest, one should apply the cross-validation selector externally to candidate bagged estimators indexed by these fine-tuning parameters. We use three simulations to compare the new cross-validated bagging method with bagging of cross-validated estimators and bagging of non-cross-validated estimators.     

Asymptotic learning on Bayesian social networks

We study a standard model of economic agents on the nodes of a social network graph who learn a binary “state of the world” $S$ , from initial signals, by repeatedly observing each other’s best guesses. Asymptotic learning is said to occur on a family of graphs $G_n = (V_n,E_n)$ with $|V_n| \rightarrow \infty $ if with probability tending to $1$ as $n \rightarrow \infty $ all agents in $G_n$ eventually estimate $S$ correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.     

Visibility graph approach to the analysis of ocean tidal records

By using the recent method of the visibility graph, three time series of oceanic tide level in central Argentina were investigated. The degree distributions show a rich structure; in particular the maximum is due to the main periodic oscillations at 24 hours and 12 hours and higher harmonics. The degree distributions of the residuals (obtained removing from the original signals the cyclic components) suggest that the local effects, linked with the particular coastal conditions of the sites, are discernible for the degree k < 20, while the global effects, linked with linked with the more general and common atmospheric forcing and ocean current conditions, are visible for k > 100. Although a relationship between the spectral exponent α and the exponent of the degree distribution γ of tidal signals can be recognized, this cannot be simply stated due to the very rich and complex structure of time dynamics of tides. The present study, even if still preliminary, show the importance of the visibility graph method in investigating the complex time dynamics of observational and experimental signals.     

Sharing costs in highways: A game theoretic approach

This paper introduces a new class of games, highway games, which arise from situations where there is a common resource that agents will jointly use. That resource is an ordered set of several indivisible sections, where each section has an associated fixed cost and each agent requires some consecutive sections. We present an easy formula to calculate the Shapley value, and we present an efficient procedure to calculate the nucleolus for this class of games.     

Structure of a class of singular boundary value problem with superlinear effect

This paper investigates the structure of solutions of singular boundary value problem with superlinear effect. It is proved that the closure of positive solution set possesses a maximal subcontinuum C (i.e., a maximal closed connected subset of solutions), which comes from (0,θ) and tends to (0,+∞) finally. As a corollary, the existence of multiple positive solutions and the behavior of solutions according to parameter λ are obtained.     

Lower bounding aggregation and direct computation for an infinite horizon one-reservoir model

We present a specialized policy iteration method for the computation of optimal and approximately optimal policies for a discrete-time model of a single reservoir whose discharges generate hydroelectric power. The model is described in (Lamond et al., 1995) and (Drouin et al., 1996), where the special structure of optimal policies is given and an approximate value iteration method is presented, using piecewise affine approximations of the optimal return functions. Here, we present a finite method for computing an optimal policy in O(n³) arithmetic operations, where n is the number of states in the associated Markov decision process, and a finite method for computing a lower bound on the optimal value function in O(m²n) where m is the number of nodes of the piecewise affine approximation.     

Parallel machine covering with limited number of preemptions简

In this paper,we investigate the i-preemptive scheduling on parallel machines to maximize the minimum machine completion time,i.e.,machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case,we show the worst case ratio is 2m.i.1 m,and we present a polynomial time algorithm which can guarantee the ratio for any 0 ≤ i ≤ m. 1. For the i-preemptive scheduling on two uniform machines case,we only need to consider the cases of i = 0 and i = 1. For both cases,we present two linear time algorithms and obtain the worst case ratios with respect to s,i.e.,the ratio of the speeds of two machines.     

Transient hydromagnetic flow in a rotating channel permeated by an inclined magnetic field with magnetic induction and Maxwell displacement current effects

Closed-form solutions are presented for the transient hydromagnetic flow in a rotating channel with inclined applied magnetic field under the influence of a forced oscillation. Magnetic Reynolds number is large enough to permit the inclusion of magnetic induction effects. The Maxwell displacement current effect is also included and simulated via a dielectric strength parameter. The governing momentum and magnetic induction conservation equations are normalized with appropriate transformations and the resulting quartet of partial differential equations are solved exactly. A parametric study is performed of the influence of oscillation frequency parameter (ω), time (T), inverse Ekman number, i.e. rotation parameter (K ²), square of the Hartmann magnetohydrodynamic (MHD) parameter (M ²), and magnetic field inclination (θ) on the primary and secondary induced magnetic field components (b _x , b _y ) and velocity components (u, v) across the channel. Network solutions are also obtained to validate the exact solutions and shown to be in excellent agreement. Applications of the study arise in planetary plasma physics and rotating MHD induction power generators and also astronautical flows.     

A semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces

We study the solvability of a semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces H_l,p,q, 1<p<∞, depending on a complex parameter q. To cite this article: Y.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Enhancing Sparsity by Reweighted ℓ 1 Minimization

It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained ? ₁ minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms ? ₁ minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted ? ₁-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations—not by reweighting the ? ₁ norm of the coefficient sequence as is common, but by reweighting the ? ₁ norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as Compressive Sensing.