7,831 research outputs found

    Gray-box optimization and factorized distribution algorithms: where two worlds collide

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    The concept of gray-box optimization, in juxtaposition to black-box optimization, revolves about the idea of exploiting the problem structure to implement more efficient evolutionary algorithms (EAs). Work on factorized distribution algorithms (FDAs), whose factorizations are directly derived from the problem structure, has also contributed to show how exploiting the problem structure produces important gains in the efficiency of EAs. In this paper we analyze the general question of using problem structure in EAs focusing on confronting work done in gray-box optimization with related research accomplished in FDAs. This contrasted analysis helps us to identify, in current studies on the use problem structure in EAs, two distinct analytical characterizations of how these algorithms work. Moreover, we claim that these two characterizations collide and compete at the time of providing a coherent framework to investigate this type of algorithms. To illustrate this claim, we present a contrasted analysis of formalisms, questions, and results produced in FDAs and gray-box optimization. Common underlying principles in the two approaches, which are usually overlooked, are identified and discussed. Besides, an extensive review of previous research related to different uses of the problem structure in EAs is presented. The paper also elaborates on some of the questions that arise when extending the use of problem structure in EAs, such as the question of evolvability, high cardinality of the variables and large definition sets, constrained and multi-objective problems, etc. Finally, emergent approaches that exploit neural models to capture the problem structure are covered.Comment: 33 pages, 9 tables, 3 figures. This paper covers some of the topics of the talk "When the gray box was opened, model-based evolutionary algorithms were already there" presented in the Model-Based Evolutionary Algorithms workshop on July 20, 2016, in Denve

    Directional Statistics on Permutations

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    Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities (n!n!). It makes the direct definition of a multinomial distribution over permutation space impractical for all but a very small nn. In this work we propose an embedding of all n!n! permutations for a given nn in a surface of a hypersphere defined in \mathbbm{R}^{(n-1)^2}. As a result of the embedding, we acquire ability to define continuous distributions over a hypersphere with all the benefits of directional statistics. We provide polynomial time projections between the continuous hypersphere representation and the n!n!-element permutation space. The framework provides a way to use continuous directional probability densities and the methods developed thereof for establishing densities over permutations. As a demonstration of the benefits of the framework we derive an inference procedure for a state-space model over permutations. We demonstrate the approach with applications

    DeepChrome: Deep-learning for predicting gene expression from histone modifications

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    Motivation: Histone modifications are among the most important factors that control gene regulation. Computational methods that predict gene expression from histone modification signals are highly desirable for understanding their combinatorial effects in gene regulation. This knowledge can help in developing 'epigenetic drugs' for diseases like cancer. Previous studies for quantifying the relationship between histone modifications and gene expression levels either failed to capture combinatorial effects or relied on multiple methods that separate predictions and combinatorial analysis. This paper develops a unified discriminative framework using a deep convolutional neural network to classify gene expression using histone modification data as input. Our system, called DeepChrome, allows automatic extraction of complex interactions among important features. To simultaneously visualize the combinatorial interactions among histone modifications, we propose a novel optimization-based technique that generates feature pattern maps from the learnt deep model. This provides an intuitive description of underlying epigenetic mechanisms that regulate genes. Results: We show that DeepChrome outperforms state-of-the-art models like Support Vector Machines and Random Forests for gene expression classification task on 56 different cell-types from REMC database. The output of our visualization technique not only validates the previous observations but also allows novel insights about combinatorial interactions among histone modification marks, some of which have recently been observed by experimental studies.Comment: This work will be originally published in Bioinformatics Journal (ECCB 2016

    DAG-GNN: DAG Structure Learning with Graph Neural Networks

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    Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that ensures acyclicity (Zheng et al., 2018). The authors apply the approach to the linear structural equation model (SEM) and the least-squares loss function that are statistically well justified but nevertheless limited. Motivated by the widespread success of deep learning that is capable of capturing complex nonlinear mappings, in this work we propose a deep generative model and apply a variant of the structural constraint to learn the DAG. At the heart of the generative model is a variational autoencoder parameterized by a novel graph neural network architecture, which we coin DAG-GNN. In addition to the richer capacity, an advantage of the proposed model is that it naturally handles discrete variables as well as vector-valued ones. We demonstrate that on synthetic data sets, the proposed method learns more accurate graphs for nonlinearly generated samples; and on benchmark data sets with discrete variables, the learned graphs are reasonably close to the global optima. The code is available at \url{https://github.com/fishmoon1234/DAG-GNN}.Comment: ICML2019. Code is available at https://github.com/fishmoon1234/DAG-GN

    Relational inductive biases, deep learning, and graph networks

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    Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice

    From Machine Learning to Machine Reasoning

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    A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes much simpler manipulations commonly used to build large learning systems. For instance, we can build an optical character recognition system by first training a character segmenter, an isolated character recognizer, and a language model, using appropriate labeled training sets. Adequately concatenating these modules and fine tuning the resulting system can be viewed as an algebraic operation in a space of models. The resulting model answers a new question, that is, converting the image of a text page into a computer readable text. This observation suggests a conceptual continuity between algebraically rich inference systems, such as logical or probabilistic inference, and simple manipulations, such as the mere concatenation of trainable learning systems. Therefore, instead of trying to bridge the gap between machine learning systems and sophisticated "all-purpose" inference mechanisms, we can instead algebraically enrich the set of manipulations applicable to training systems, and build reasoning capabilities from the ground up.Comment: 15 pages - fix broken pagination in v

    Machine Learning Methods for Data Association in Multi-Object Tracking

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    Data association is a key step within the multi-object tracking pipeline that is notoriously challenging due to its combinatorial nature. A popular and general way to formulate data association is as the NP-hard multidimensional assignment problem (MDAP). Over the last few years, data-driven approaches to assignment have become increasingly prevalent as these techniques have started to mature. We focus this survey solely on learning algorithms for the assignment step of multi-object tracking, and we attempt to unify various methods by highlighting their connections to linear assignment as well as to the MDAP. First, we review probabilistic and end-to-end optimization approaches to data association, followed by methods that learn association affinities from data. We then compare the performance of the methods presented in this survey, and conclude by discussing future research directions.Comment: Accepted for publication in ACM Computing Survey

    An Atomistic Machine Learning Package for Surface Science and Catalysis

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    We present work flows and a software module for machine learning model building in surface science and heterogeneous catalysis. This includes fingerprinting atomic structures from 3D structure and/or connectivity information, it includes descriptor selection methods and benchmarks, and it includes active learning frameworks for atomic structure optimization, acceleration of screening studies and for exploration of the structure space of nano particles, which are all atomic structure problems relevant for surface science and heterogeneous catalysis. Our overall goal is to provide a repository to ease machine learning model building for catalysis, to advance the models beyond the chemical intuition of the user and to increase autonomy for exploration of chemical space

    Robust Continuous Co-Clustering

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    Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous Co-Clustering algorithm. ROCCO is a scalable, hyperparameter-free, easy and ready to use algorithm to address Co-Clustering problems in practice over massive cross-domain datasets. It operates by learning a graph-based two-sided representation of the input matrix. The underlying proposed optimization problem is non-convex, which assures a flexible pool of solutions. Moreover, we prove that it can be solved with a near linear time complexity on the input size. An exhaustive large-scale experimental testbed conducted with both synthetic and real-world datasets demonstrates ROCCO's properties in practice: (i) State-of-the-art performance in cross-domain real-world problems including Biomedicine and Text Mining; (ii) very low sensitivity to hyperparameter settings; (iii) robustness to noise and (iv) a linear empirical scalability in practice. These results highlight ROCCO as a powerful general-purpose co-clustering algorithm for cross-domain practitioners, regardless of their technical background.Comment: Under reviewing proces

    Inference in Graphical Models via Semidefinite Programming Hierarchies

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    Maximum A posteriori Probability (MAP) inference in graphical models amounts to solving a graph-structured combinatorial optimization problem. Popular inference algorithms such as belief propagation (BP) and generalized belief propagation (GBP) are intimately related to linear programming (LP) relaxation within the Sherali-Adams hierarchy. Despite the popularity of these algorithms, it is well understood that the Sum-of-Squares (SOS) hierarchy based on semidefinite programming (SDP) can provide superior guarantees. Unfortunately, SOS relaxations for a graph with nn vertices require solving an SDP with nΘ(d)n^{\Theta(d)} variables where dd is the degree in the hierarchy. In practice, for d≥4d\ge 4, this approach does not scale beyond a few tens of variables. In this paper, we propose binary SDP relaxations for MAP inference using the SOS hierarchy with two innovations focused on computational efficiency. Firstly, in analogy to BP and its variants, we only introduce decision variables corresponding to contiguous regions in the graphical model. Secondly, we solve the resulting SDP using a non-convex Burer-Monteiro style method, and develop a sequential rounding procedure. We demonstrate that the resulting algorithm can solve problems with tens of thousands of variables within minutes, and outperforms BP and GBP on practical problems such as image denoising and Ising spin glasses. Finally, for specific graph types, we establish a sufficient condition for the tightness of the proposed partial SOS relaxation
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