Short-Time Scaling of Variable Orderingof OBDDs

A short-time scaling criterion of variable ordering of OBDDs is proposed.By this criterion it is easy and fast to determine which one is better when several variable orders are given,especially when they differ 10% or more in resulted BDD size from each other.An adaptive variable order selection method,based on the short-time scaling criterion,is also presented.The experimental results show that this method is efficient and it makes the heuristic variable ordering methods more practical.     

Multiagent learning using a variable learning rate

Learning to act in a multiagent environment is a difficult problem since the normal definition of an optimal policy no longer applies. The optimal policy at any moment depends on the policies of the other agents. This creates a situation of learning a moving target. Previous learning algorithms have one of two shortcomings depending on their approach. They either converge to a policy that may not be optimal against the specific opponents' policies, or they may not converge at all. In this article we examine this learning problem in the framework of stochastic games. We look at a number of previous learning algorithms showing how they fail at one of the above criteria. We then contribute a new reinforcement learning technique using a variable learning rate to overcome these shortcomings. Specifically, we introduce the WoLF principle, “Win or Learn Fast”, for varying the learning rate. We examine this technique theoretically, proving convergence in self-play on a restricted class of iterated matrix games. We also present empirical results on a variety of more general stochastic games, in situations of self-play and otherwise, demonstrating the wide applicability of this method.     

On the size of (generalized) OBDDs for threshold functions

Ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Among the many areas of application are hardware verification, model checking, and symbolic graph algorithms. Threshold functions are the basic functions for discrete neural networks and are used as building blocks in the design of some symbolic graph algorithms. In this paper the first exponential lower bound on the size of a more general model than OBDDs and the first nontrivial asymptotically optimal bound on the OBDD size for a threshold function are presented.     

On the size of randomized OBDDs and read-once branching programs for k-stable functions

In this paper, a simple technique which unifies the known approaches for proving lower bound results on the size of deterministic, nondeterministic, and randomized OBDDs and kOBDDs is described.?As an application of this technique, a generic lower bound on the size of randomized OBDDs with bounded error is established for a class of functions which has been studied in the literature on branching programs for a long time. These functions have been called “k-stable” by Jukna. It follows that several standard functions are not contained in the analog of the class BPP for OBDDs. Furthermore, exponential lower bounds on the size of randomized kOBDDs are presented.?It is well known that k-stable functions with large k are hard for deterministic read-once branching programs. This is no longer true in the randomized case. It is shown here that a certain k-stable function due to Jukna, Razborov, Savicky, and Wegener has randomized branching programs of polynomial size, even with zero error. It follows that for the analogs of these classes defined in terms of the size of read-once branching programs. Received: September 3, 1998.     

Minimal ordering constraints for some families of variable symmetries

Variable symmetries in a constraint satisfaction problem can be broken by adding lexicographic ordering constraints. Existing general methods of generating such sets of ordering constraints can require a huge number of constraints. This adds an unacceptable overhead to the solving process. Methods exist by which this large set of ordering constraints can be reduced to a much smaller set automatically, but their application is also prohibitively costly. In contrast, this paper takes a bottom-up approach. It examines some commonly-occurring families of groups and derives a minimal set of ordering constraints sufficient to break the symmetry each group describes. These minimal sets are then used as building blocks to generate minimal sets of ordering constraints for groups constructed via direct and imprimitive wreath products. Experimental results confirm the value of minimal sets of ordering constraints, which can now be generated much more cheaply than with previous methods.     

On the algorithmic implementation of stochastic discrimination

Stochastic discrimination is a general methodology for constructing classifiers appropriate for pattern recognition. It is based on combining arbitrary numbers of very weak components, which are usually generated by some pseudorandom process, and it has the property that the very complex and accurate classifiers produced in this way retain the ability, characteristic of their weak component pieces, to generalize to new data. In fact, it is often observed, in practice, that classifier performance on test sets continues to rise as more weak components are added, even after performance on training sets seems to have reached a maximum. This is predicted by the underlying theory, for even though the formal error rate on the training set may have reached a minimum, more sophisticated measures intrinsic to this method indicate that classifier performance on both training and test sets continues to improve as complexity increases. We begin with a review of the method of stochastic discrimination as applied to pattern recognition. Through a progression of examples keyed to various theoretical issues, we discuss considerations involved with its algorithmic implementation. We then take such an algorithmic implementation and compare its performance, on a large set of standardized pattern recognition problems from the University of California Irvine, and Statlog collections, to many other techniques reported on in the literature, including boosting and bagging. In doing these studies, we compare our results to those reported in the literature by the various authors for the other methods, using the same data and study paradigms used by them. Included in the paper is an outline of the underlying mathematical theory of stochastic discrimination and a remark concerning boosting, which provides a theoretical justification for properties of that method observed in practice, including its ability to generalize     

On the numerical stability of algorithmic differentiation

In contrast to integration, the differentiation of a function is an ill-conditioned process, if only an oracle is available for its pointwise evaluation. That is, unrelated small variations in the value of the composite function are allowed at nearly identical arguments. In contrast, we show here that, if the function is defined by an evaluation procedure as a composition of arithmetic operations and elementary functions, then automatic, or algorithmic differentiation is backward stable in the sense of Wilkinson. More specifically, the derivative values obtained are exact for a perturbation of the elementary components at the level of the machine precision. We also provide a forward error analysis for both the forward and reverse mode. The theoretical analysis is confirmed by numerical experiments.     

On the algorithmic complexity of associative algebras

The complexity L(A) of a finite dimensional associative algebra A is the number of non-scalar multiplications/divisions of an optimal algorithm to compute the product of two elements of the algebra. We show

$\text{L(A) ? 2ddim A?t}$

, where t is the number of maximal two-sided ideals of A.     

On the Power of Las Vegas for One-Way Communication Complexity, OBDDs, and Finite Automata

The study of the computational power of randomized computations is one of the central tasks of complexity theory. The main goal of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation. We investigate the power of Las Vegas computation for the complexity measures of one-way communication, ordered binary decision diagrams, and finite automata.(i) For the one-way communication complexity of two-party protocols we show that Las Vegas communication can save at most one half of the deterministic one-way communication complexity. We also present a language for which this gap is tight.(ii) The result (i) is applied to show an at most polynomial gap between determinism and Las Vegas for ordered binary decision diagrams.(iii) For the size (i.e., the number of states) of finite automata we show that the size of Las Vegas finite automata recognizing a language L is at least the square root of the size of the minimal deterministic finite automaton recognizing L. Using a specific language we verify the optimality of this lower bound.     

Efficient algorithmic learning of the structure of permutation groups by examples

This paper discusses learning algorithms for ascertaining membership, inclusion, and equality in permutation groups. The main results are randomized learning algorithms which take a random generator set of a fixed group G ≤ S_n as input. We discuss randomized algorithms for learning the concepts of group membership, inclusion, and equality by representing the group in terms of its strong sequence of generators using random examples from G. We present O(n³ log n) time sequential learning algorithms for testing membership, inclusion and equality. The running time is expressed as a function of the size of the object set. (G ≤ S_n can have as many as n! elements.) Our bounds hold for all input groups. We also introduce limited parallelism, and our lower processor bounds make our algorithms more practical.Finally, we show that learning two-groups is in class NC by reducing the membership, inclusion, and inequality problems to solving linear systems over GF(2). We present an O(log³ n) time learning algorithm using n^ω processors for learning two-groups from examples (where n × n matrix product takes logarithmic time using n^ω processors).     

基于半监督学习的链接预测算法的研究*

针对链接挖掘中网络的结构难以预测这个难点问题,提出了一个关于链接预测的新型半监督学习方法——基于快速共轭梯度方法和链接相似性传递增殖原理的链接预测算法,利用节点相似性等辅助信息去预测未知结构。该算法利用张量的形式去表示多维的复杂的多关系数据,利用克罗内克积与克罗内克和去计算张量之间的相似性,利用向量特技方法降低了算法的时间和空间复杂度。在社会网络和生物信息网络等环境下,通过实验验证了算法的有效性和健壮性。     

A note on the size of OBDDs for the graph of integer multiplication

Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are the most common dynamic data structure for Boolean functions. Among the many areas of application are verification, model checking, computer-aided design, relational algebra, and symbolic graph algorithms. Analyzing the limits of symbolic graph algorithms for the all-pairs-shortest paths problem which work on OBDD-represented graph instances the so-called graph of integer multiplication has been investigated by Sawitzki [D. Sawitzki, Lower bounds on the OBDD size of graphs of some popular functions, in: Proc. of SOFSEM, LNCS, vol. 3381, 2005, pp. 298-309]. Using simple arguments his lower bound of ²n/768−1 on the size of OBDDs representing the graph of integer multiplication is improved up to ²n/24.     

A general criterion and an algorithmic framework for learning in multi-agent systems

We offer a new formal criterion for agent-centric learning in multi-agent systems, that is, learning that maximizes one’s rewards in the presence of other agents who might also be learning (using the same or other learning algorithms). This new criterion takes in as a parameter the class of opponents. We then provide a modular approach for achieving effective agent-centric learning; the approach consists of a number of basic algorithmic building blocks, which can be instantiated and composed differently depending on the environment setting (for example, 2- versus n-player games) as well as the target class of opponents. We then provide several specific instances of the approach: an algorithm for stationary opponents, and two algorithms for adaptive opponents with bounded memory, one algorithm for the n-player case and another optimized for the 2-player case. We prove our algorithms correct with respect to the formal criterion, and furthermore show the algorithms to be experimentally effective via comprehensive computer testing.     

On some classes of algorithmic algebras

Two classes of algorithmic algebras are studied: S^*-algebras, which are a direct generalization of S-algebras (algebras with closed conditions), and Markov systems of algorithmic algebras (a stochastic version of algorithmic algebras).Translated from Kibernetika, No. 3, pp. 100–104, May–June 1990.     

Flexible latent variable models for multi-task learning

Given multiple prediction problems such as regression or classification, we are interested in a joint inference framework that can effectively share information between tasks to improve the prediction accuracy, especially when the number of training examples per problem is small. In this paper we propose a probabilistic framework which can support a set of latent variable models for different multi-task learning scenarios. We show that the framework is a generalization of standard learning methods for single prediction problems and it can effectively model the shared structure among different prediction tasks. Furthermore, we present efficient algorithms for the empirical Bayes method as well as point estimation. Our experiments on both simulated datasets and real world classification datasets show the effectiveness of the proposed models in two evaluation settings: a standard multi-task learning setting and a transfer learning setting.     

Robust technical trading strategies using GP for algorithmic portfolio selection

This paper presents a Robust Genetic Programming approach for discovering profitable trading rules which are used to manage a portfolio of stocks from the Spanish market. The investigated method is used to determine potential buy and sell conditions for stocks, aiming to yield robust solutions able to withstand extreme market conditions, while producing high returns at a minimal risk. One of the biggest challenges GP evolved solutions face is over-fitting. GP trading rules need to have similar performance when tested with new data in order to be deployed in a real situation. We explore a random sampling method (RSFGP) which instead of calculating the fitness over the whole dataset, calculates it on randomly selected segments. This method shows improved robustness and out-of-sample results compared to standard genetic programming (SGP) and a volatility adjusted fitness (VAFGP). Trading strategies (TS) are evolved using financial metrics like the volatility, CAPM alpha and beta, and the Sharpe ratio alongside other Technical Indicators (TI) to find the best investment strategy. These strategies are evaluated using 21 of the most liquid stocks of the Spanish market. The achieved results clearly outperform Buy&Hold, SGP and VAFGP. Additionally, the solutions obtained with the training data during the experiments clearly show during testing robustness to step market declines as seen during the European sovereign debt crisis experienced recently in Spain. In this paper the solutions learned were able to operate for prolonged periods, which demonstrated the validity and robustness of the rules learned, which are able to operate continuously and with minimal human intervention. To sum up, the developed method is able to evolve TSs suitable for all market conditions with promising results, which suggests great potential in the method generalization capabilities. The use of financial metrics alongside popular TI enables the system to increase the stock return while proving resilient through time. The RSFGP system is able to cope with different types of markets achieving a portfolio return of 31.81% for the testing period 2009–2013 in the Spanish market, having the IBEX35 index returned 2.67%.     

Coordinated ordering decisions for products with short lifecycle and variable selling price

The supplier–buyer coordination is an important policy in the supply chain management. The buyer in the two-echelon inventory system with regular selling season has to face the uncertainty of customer demand, supplier’s delivery time and variable price change. At the same time, the supplier has to consider the inventory holding and delay cost. The objective of this study is to develop an integrated supply chain strategy for products with short lifecycle and variable selling price to entice cooperation. The strategy must provide a win–win situation for both the supplier and the buyer. A numerical case example, sensitivity analysis and compensation mechanism are given to illustrate the model.     

Randomized OBDDs for the most significant bit of multiplication need exponential space

Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Only in 2008 the question whether the deterministic OBDD complexity of the most significant bit of integer multiplication is exponential has been answered affirmatively. Since probabilistic methods have turned out to be useful in almost all areas of computer science, one may ask whether randomization can help to represent the most significant bit of integer multiplication in smaller size. Here, it is proved that the randomized OBDD complexity is also exponential.     

An algorithmic theory of learning: Robust concepts and random projection

We study the phenomenon of cognitive learning from an algorithmic standpoint. How does the brain effectively learn concepts from a small number of examples despite the fact that each example contains a huge amount of information? We provide a novel algorithmic analysis via a model of robust concept learning (closely related to “margin classifiers”), and show that a relatively small number of examples are sufficient to learn rich concept classes. The new algorithms have several advantages—they are faster, conceptually simpler, and resistant to low levels of noise. For example, a robust half-space can be learned in linear time using only a constant number of training examples, regardless of the number of attributes. A general (algorithmic) consequence of the model, that “more robust concepts are easier to learn”, is supported by a multitude of psychological studies.     

Formal Derivation of Graph AlgorithmicPrograms Using Partition-and-Recur

In this paper,we derive,by presenting some suitable notations,three typical graph algorithms and corresponding programs using a unified approach,partition-and-recur.We putemphasis on the derivation rather than the algorithms themselves.The main ideas and ingenuity of these algorithms are revealed by formula deduction.Success in these examples gives us more evidence that partition-and-recur is a simple and practical approach and developing enough suitable notations is the key in designing and deriving efficient and correct algorithmic programs.