Combinatorial optimization problems require an exhaustive search to find the optimal solution. A convenient approach to solving combinatorial optimization tasks in the form of Mixed Integer Linear Programs is Branch-and-Bound. Branch-and-Bound solver splits a task into two parts dividing the domain of an integer variable, then it solves them recursively, producing a tree of nested sub-tasks. The efficiency of the solver depends on the branchning heuristic used to select a variable for splitting. In the present work, we propose a reinforcement learning method that can efficiently learn the branching heuristic. We view the variable selection task as a tree Markov Decision Process, prove that the Bellman operator adapted for the tree Markov Decision Process is contracting in mean, and propose a modified learning objective for the reinforcement learning agent. Our agent requires less training data and produces smaller trees compared to previous reinforcement learning methods.
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Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable discretization space, and next perform a Galerkin approximation of the problem on that space. We investigate here how these approaches can be implemented in a non-intrusive way, in order to facilitate their dissemination within industrial codes or non-academic environments. We develop an abstract framework that covers a wide variety of MsFEMs for linear second-order partial differential equations. Non-intrusive MsFEM approaches are developed within the full generality of this framework, which may moreover be beneficial to steering software development and improving the theoretical understanding and analysis of MsFEMs.
A common way to evaluate the reliability of dimensionality reduction (DR) embeddings is to quantify how well labeled classes form compact, mutually separated clusters in the embeddings. This approach is based on the assumption that the classes stay as clear clusters in the original high-dimensional space. However, in reality, this assumption can be violated; a single class can be fragmented into multiple separated clusters, and multiple classes can be merged into a single cluster. We thus cannot always assure the credibility of the evaluation using class labels. In this paper, we introduce two novel quality measures -- Label-Trustworthiness and Label-Continuity (Label-T&C) -- advancing the process of DR evaluation based on class labels. Instead of assuming that classes are well-clustered in the original space, Label-T&C work by (1) estimating the extent to which classes form clusters in the original and embedded spaces and (2) evaluating the difference between the two. A quantitative evaluation showed that Label-T&C outperform widely used DR evaluation measures (e.g., Trustworthiness and Continuity, Kullback-Leibler divergence) in terms of the accuracy in assessing how well DR embeddings preserve the cluster structure, and are also scalable. Moreover, we present case studies demonstrating that Label-T&C can be successfully used for revealing the intrinsic characteristics of DR techniques and their hyperparameters.
We describe recent research on the use of actual causality in the definition of responsibility scores as explanations for query answers in databases, and for outcomes from classification models in machine learning. In the case of databases, useful connections with database repairs are illustrated and exploited. Repairs are also used to give a quantitative measure of the consistency of a database. For classification models, the responsibility score is properly extended and illustrated. The efficient computation of Shap-score is also analyzed and discussed. The emphasis is placed on work done by the author and collaborators.
Compared to mean regression and quantile regression, the literature on modal regression is very sparse. We propose a unified framework for Bayesian modal regression based on a family of unimodal distributions indexed by the mode along with other parameters that allow for flexible shapes and tail behaviors. Following prior elicitation, we carry out regression analysis of simulated data and datasets from several real-life applications. Besides drawing inference for covariate effects that are easy to interpret, we consider prediction and model selection under the proposed Bayesian modal regression framework. Evidence from these analyses suggest that the proposed inference procedures are very robust to outliers, enabling one to discover interesting covariate effects missed by mean or median regression, and to construct much tighter prediction intervals than those from mean or median regression. Computer programs for implementing the proposed Bayesian modal regression are available at //github.com/rh8liuqy/Bayesian_modal_regression.
Which technological linkages affect the sector's ability to innovate? How do these effects transmit through the technology space? This paper answers these two key questions using novel methods of text mining and network analysis. We examine technological interdependence across sectors over a period of half a century (from 1976 to 2021) by analyzing the text of 6.5 million patents granted by the United States Patent and Trademark Office (USPTO), and applying network analysis to uncover the full spectrum of linkages existing across technology areas. We demonstrate that patent text contains a wealth of information often not captured by traditional innovation metrics, such as patent citations. By using network analysis, we document that indirect linkages are as important as direct connections and that the former would remain mostly hidden using more traditional measures of indirect linkages, such as the Leontief inverse matrix. Finally, based on an impulse-response analysis, we illustrate how technological shocks transmit through the technology (network-based) space, affecting the innovation capacity of the sectors.
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence or absence of general group symmetry, however, are largely non-existent. This work formulates non-parametric hypothesis tests, based on a single independent and identically distributed sample, for distributional symmetry under a specified group. We provide a general formulation of tests for symmetry that apply to two broad settings. The first setting tests for the invariance of a marginal or joint distribution under the action of a compact group. Here, an asymptotically unbiased test only requires a computable metric on the space of probability distributions and the ability to sample uniformly random group elements. Building on this, we propose an easy-to-implement conditional Monte Carlo test and prove that it achieves exact $p$-values with finitely many observations and Monte Carlo samples. The second setting tests for the invariance or equivariance of a conditional distribution under the action of a locally compact group. We show that the test for conditional invariance or equivariance can be formulated as particular tests of conditional independence. We implement these tests from both settings using kernel methods and study them empirically on synthetic data. Finally, we apply them to testing for symmetry in geomagnetic satellite data and in two problems from high-energy particle physics.
Synthesis of distributed protocols is a hard, often undecidable, problem. Completion techniques provide partial remedy by turning the problem into a search problem. However, the space of candidate completions is still massive. In this paper, we propose optimization techniques to reduce the size of the search space by a factorial factor by exploiting symmetries (isomorphisms) in functionally equivalent solutions. We present both a theoretical analysis of this optimization as well as empirical results that demonstrate its effectiveness in synthesizing both the Alternating Bit Protocol and Two Phase Commit. Our experiments show that the optimized tool achieves a speedup of approximately 2 to 10 times compared to its unoptimized counterpart.
Human interactions create social networks forming the backbone of societies. Individuals adjust their opinions by exchanging information through social interactions. Two recurrent questions are whether social structures promote opinion polarisation or consensus in societies and whether polarisation can be avoided, particularly on social media. In this paper, we hypothesise that not only network structure but also the timings of social interactions regulate the emergence of opinion clusters. We devise a temporal version of the Deffuant opinion model where pairwise interactions follow temporal patterns and show that burstiness alone is sufficient to refrain from consensus and polarisation by promoting the reinforcement of local opinions. Individuals self-organise into a multi-partisan society due to network clustering, but the diversity of opinion clusters further increases with burstiness, particularly when individuals have low tolerance and prefer to adjust to similar peers. The emergent opinion landscape is well-balanced regarding clusters' size, with a small fraction of individuals converging to extreme opinions. We thus argue that polarisation is more likely to emerge in social media than offline social networks because of the relatively low social clustering observed online. Counter-intuitively, strengthening online social networks by increasing social redundancy may be a venue to reduce polarisation and promote opinion diversity.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.
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