OpenRaiser/Intern-Atlas huggingface dataset:
Efficient Reinforcement Learning in Deterministic Systems with Value Function Generalization
Venue: arXiv cs.LG 2016
Year: 2016

We consider the problem of reinforcement learning over episodes of a finite-horizon deterministic system and as a solution propose optimistic constraint propagation (OCP), an algorithm designed to synthesize efficient exploration and value function generalization. We establish that when the true value function lies within a given hypothesis class, OCP selects optimal actions over all but at most K episodes, where K is the eluder dimension of the given hypothesis class. We establish further efficiency and asymptotic performance guarantees that apply even if the true value function does not lie in the given hypothesis class, for the special case where the hypothesis class is the span of pre-specified indicator functions over disjoint sets. We also discuss the computational complexity of OCP and present computational results involving two illustrative examples.
Coded Caching with Nonuniform Demands
Venue: arXiv cs.IT 2016
Year: 2016

We consider a network consisting of a file server connected through a shared link to a number of users, each equipped with a cache. Knowing the popularity distribution of the files, the goal is to optimally populate the caches such as to minimize the expected load of the shared link. For a single cache, it is well known that storing the most popular files is optimal in this setting. However, we show here that this is no longer the case for multiple caches. Indeed, caching only the most popular files can be highly suboptimal. Instead, a fundamentally different approach is needed, in which the cache contents are used as side information for coded communication over the shared link. We propose such a coded caching scheme and prove that it is close to optimal.
Average Drift Analysis and Population Scalability
Venue: arXiv cs.NE 2016
Year: 2016

This paper aims to study how the population size affects the computation time of evolutionary algorithms in a rigorous way. The computation time of an evolutionary algorithm can be measured by either the expected number of generations (hitting time) or the expected number of fitness evaluations (running time) to find an optimal solution. Population scalability is the ratio of the expected hitting time between a benchmark algorithm and an algorithm using a larger population size. Average drift analysis is presented for comparing the expected hitting time of two algorithms and estimating lower and upper bounds on population scalability. Several intuitive beliefs are rigorously analysed. It is prove that (1) using a population sometimes increases rather than decreases the expected hitting time; (2) using a population cannot shorten the expected running time of any elitist evolutionary algorithm on unimodal functions in terms of the time-fitness landscape, but this is not true in terms of the distance-based fitness landscape; (3) using a population cannot always reduce the expected running time on fully-deceptive functions, which depends on the benchmark algorithm using elitist selection or random selection.
Palindrome Recognition In The Streaming Model
Venue: arXiv cs.DS 2016
Year: 2016

In the Palindrome Problem one tries to find all palindromes (palindromic substrings) in a given string. A palindrome is defined as a string which reads forwards the same as backwards, e.g., the string "racecar". A related problem is the Longest Palindromic Substring Problem in which finding an arbitrary one of the longest palindromes in the given string suffices. We regard the streaming version of both problems. In the streaming model the input arrives over time and at every point in time we are only allowed to use sublinear space. The main algorithms in this paper are the following: The first one is a one-pass randomized algorithm that solves the Palindrome Problem. It has an additive error and uses $O(\sqrt n$) space. The second algorithm is a two-pass algorithm which determines the exact locations of all longest palindromes. It uses the first algorithm as the first pass. The third algorithm is again a one-pass randomized algorithm, which solves the Longest Palindromic Substring Problem. It has a multiplicative error using only $O(\log(n))$ space. We also give two variants of the first algorithm which solve other related practical problems.
Online and stochastic Douglas-Rachford splitting method for large scale machine learning
Venue: arXiv cs.NA 2016
Year: 2016

Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version). We first establish an $O(1/\sqrt{T})$ regret bound for batch DRs method. Then we proved that the online DRs splitting method enjoy an $O(1)$ regret bound and stochastic DRs splitting has a convergence rate of $O(1/\sqrt{T})$. The proof is simple and intuitive, and the results and technique can be served as a initiate for the research on the large scale machine learning employ the DRs method. Numerical experiments of the proposed method demonstrate the effectiveness of the online and stochastic update rule, and further confirm our regret and convergence analysis.
A Multiscale Pyramid Transform for Graph Signals
Venue: arXiv cs.IT 2016
Year: 2016

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric structure of the underlying graph data domain. In this paper, we adapt the Laplacian pyramid transform for signals on Euclidean domains so that it can be used to analyze high-dimensional data residing on the vertices of a weighted graph. Our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling, graph reduction, and filtering and interpolation of signals on graphs. Equipped with appropriate notions of these operations, we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs.
Fractal dimension versus process complexity
Venue: arXiv cs.CC 2016
Year: 2016

Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields are related to each other in a non-trivial fashion. Here we study small Turing machines (TMs) with two symbols, and two and three states. For any particular such machine $τ$ and any particular input $x$ we consider what we call the 'space-time' diagram which is the collection of consecutive tape configurations of the computation $τ(x)$. In our setting, we define fractal dimension of a Turing machine as the limiting fractal dimension of the corresponding space-time diagram. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the above-specified type and its runtime complexity. In particular, a TM with three states and two colors runs in at most linear time iff its dimension is 2, and its dimension is 1 iff it runs in super-polynomial time and it uses polynomial space. If a TM runs in time $O(x^n)$ we have empirically verified that the corresponding dimension is $(n+1)/n$, a result that we can only partially prove. We find the results presented here remarkable because they relate two completely different complexity measures: the geometrical fractal dimension on the one side versus the time complexity of a computation on the other side.
O-notation in algorithm analysis
Venue: arXiv cs.DS 2016
Year: 2016

We provide an extensive list of desirable properties for an O-notation --- as used in algorithm analysis --- and reduce them to 8 primitive properties. We prove that the primitive properties are equivalent to the definition of the O-notation as linear dominance. We abstract the existing definitions of the O-notation under local linear dominance, and show that it has a characterization by limits over filters for positive functions. We define the O-mappings as a general tool for manipulating the O-notation, and show that Master theorems hold under linear dominance.
Relative Deviation Learning Bounds and Generalization with Unbounded Loss Functions
Venue: arXiv cs.LG 2016
Year: 2016

We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of unbounded loss functions, under the assumption that a moment of the loss is bounded. These bounds are useful in the analysis of importance weighting and other learning tasks such as unbounded regression.
The optimality of attaching unlinked labels to unlinked meanings
Venue: arXiv cs.CL 2016
Year: 2016

Vocabulary learning by children can be characterized by many biases. When encountering a new word, children as well as adults, are biased towards assuming that it means something totally different from the words that they already know. To the best of our knowledge, the 1st mathematical proof of the optimality of this bias is presented here. First, it is shown that this bias is a particular case of the maximization of mutual information between words and meanings. Second, the optimality is proven within a more general information theoretic framework where mutual information maximization competes with other information theoretic principles. The bias is a prediction from modern information theory. The relationship between information theoretic principles and the principles of contrast and mutual exclusivity is also shown.
Using higher-order contracts to model session types
Venue: arXiv cs.LO 2016
Year: 2016

Session types are used to describe and structure interactions between independent processes in distributed systems. Higher-order types are needed in order to properly structure delegation of responsibility between processes. In this paper we show that higher-order web-service contracts can be used to provide a fully-abstract model of recursive higher-order session types. The model is set-theoretic, in the sense that the meaning of a contract is given in terms of the set of contracts with which it complies. The proof of full-abstraction depends on a novel notion of the complement of a contract. This in turn gives rise to an alternative to the type duality commonly used in systems for type-checking session types. We believe that the notion of complement captures more faithfully the behavioural intuition underlying type duality.
Dissociation and Propagation for Approximate Lifted Inference with Standard Relational Database Management Systems
Venue: arXiv cs.DB 2016
Year: 2016

Probabilistic inference over large data sets is a challenging data management problem since exact inference is generally #P-hard and is most often solved approximately with sampling-based methods today. This paper proposes an alternative approach for approximate evaluation of conjunctive queries with standard relational databases: In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema information to enumerate only the minimal necessary plans among all possible plans. Importantly, this algorithm is a strict generalization of all known PTIME self-join-free conjunctive queries: A query is in PTIME if and only if our algorithm returns one single plan. Furthermore, our approach is a generalization of a family of efficient ranking methods from graphs to hypergraphs. We also adapt three relational query optimization techniques to evaluate all necessary plans very fast. We give a detailed experimental evaluation of our approach and, in the process, provide a new way of thinking about the value of probabilistic methods over non-probabilistic methods for ranking query answers. We also note that the techniques developed in this paper apply immediately to lifted inference from statistical relational models since lifted inference corresponds to PTIME plans in probabilistic databases.
Linear Convergence of Comparison-based Step-size Adaptive Randomized Search via Stability of Markov Chains
Venue: arXiv cs.NA 2016
Year: 2016

In this paper, we consider comparison-based adaptive stochastic algorithms for solving numerical optimisation problems. We consider a specific subclass of algorithms that we call comparison-based step-size adaptive randomized search (CB-SARS), where the state variables at a given iteration are a vector of the search space and a positive parameter, the step-size, typically controlling the overall standard deviation of the underlying search distribution.We investigate the linear convergence of CB-SARS on\emph{scaling-invariant} objective functions. Scaling-invariantfunctions preserve the ordering of points with respect to their functionvalue when the points are scaled with the same positive parameter (thescaling is done w.r.t. a fixed reference point). This class offunctions includes norms composed with strictly increasing functions aswell as many non quasi-convex and non-continuousfunctions. On scaling-invariant functions, we show the existence of ahomogeneous Markov chain, as a consequence of natural invarianceproperties of CB-SARS (essentially scale-invariance and invariance tostrictly increasing transformation of the objective function). We thenderive sufficient conditions for \emph{global linear convergence} ofCB-SARS, expressed in terms of different stability conditions of thenormalised homogeneous Markov chain (irreducibility, positivity, Harrisrecurrence, geometric ergodicity) and thus define a general methodologyfor proving global linear convergence of CB-SARS algorithms onscaling-invariant functions. As a by-product we provide aconnexion between comparison-based adaptive stochasticalgorithms and Markov chain Monte Carlo algorithms.
Improved Approximation Algorithms for Matroid and Knapsack Median Problems and Applications
Venue: arXiv cs.DS 2016
Year: 2016

We consider the {\em matroid median} problem \cite{KrishnaswamyKNSS11}, wherein we are given a set of facilities with opening costs and a matroid on the facility-set, and clients with demands and connection costs, and we seek to open an independent set of facilities and assign clients to open facilities so as to minimize the sum of the facility-opening and client-connection costs. We give a simple 8-approximation algorithm for this problem based on LP-rounding, which improves upon the 16-approximation in \cite{KrishnaswamyKNSS11}. Our techniques illustrate that much of the work involved in the rounding algorithm of in \cite{KrishnaswamyKNSS11} can be avoided by first converting the LP solution to a half-integral solution, which can then be rounded to an integer solution using a simple uncapacitated-facility-location (UFL) style clustering step. We illustrate the power of these ideas by deriving: (a) a 24-approximation algorithm for matroid median with penalties, which is a vast improvement over the 360-approximation obtained in \cite{KrishnaswamyKNSS11}; and (b) an 8-approximation for the {\em two-matroid median} problem, a generalization of matroid median that we introduce involving two matroids. We show that a variety of seemingly disparate facility-location problems considered in the literature---data placement problem, mobile facility location, $k$-median forest, metric uniform minimum-latency UFL---in fact reduce to the matroid median or two-matroid median problems, and thus obtain improved approximation guarantees for all these problems. Our techniques also yield an improvement for the knapsack median problem.
Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel
Venue: arXiv cs.IT 2016
Year: 2016

We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) code ensembles defined over the general linear group on the binary erasure channel. In particular, we prove threshold saturation of belief propagation decoding to the so called potential threshold, using the proof technique based on potential functions introduced by Yedla \textit{et al.}, assuming that the potential function exists. We rewrite the density evolution of nonbinary SC-LDPC codes in an equivalent vector recursion form which is suited for the use of the potential function. We then discuss the existence of the potential function for the general case of vector recursions defined by multivariate polynomials, and give a method to construct it. We define a potential function in a slightly more general form than one by Yedla \textit{et al.}, in order to make the technique based on potential functions applicable to the case of nonbinary LDPC codes. We show that the potential function exists if a solution to a carefully designed system of linear equations exists. Furthermore, we show numerically the existence of a solution to the system of linear equations for a large number of nonbinary LDPC code ensembles, which allows us to define their potential function and thus prove threshold saturation.
Ferromagnetic Potts Model: Refined #BIS-hardness and Related Results
Venue: arXiv cs.CC 2016
Year: 2016

Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase transition on the infinite D-regular tree. For the ferromagnetic Potts model we investigate whether analogous hardness results hold. Goldberg and Jerrum showed that approximating the partition function of the ferromagnetic Potts model is at least as hard as approximating the number of independent sets in bipartite graphs (#BIS-hardness). We improve this hardness result by establishing it for bipartite graphs of maximum degree D. We first present a detailed picture for the phase diagram for the infinite D-regular tree, giving a refined picture of its first-order phase transition and establishing the critical temperature for the coexistence of the disordered and ordered phases. We then prove for all temperatures below this critical temperature that it is #BIS-hard to approximate the partition function on bipartite graphs of maximum degree D. As a corollary, it is #BIS-hard to approximate the number of k-colorings on bipartite graphs of maximum degree D when k <= D/(2 ln D). The #BIS-hardness result for the ferromagnetic Potts model uses random bipartite regular graphs as a gadget in the reduction. The analysis of these random graphs relies on recent connections between the maxima of the expectation of their partition function, attractive fixpoints of the associated tree recursions, and induced matrix norms. We extend these connections to random regular graphs for all ferromagnetic models and establish the Bethe prediction for every ferromagnetic spin system on random regular graphs. We also prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for large q.
Clique-Stable Set separation in perfect graphs with no balanced skew-partitions
Venue: arXiv cs.DM 2016
Year: 2016

Inspired by a question of Yannakakis on the Vertex Packing polytope of perfect graphs, we study the Clique-Stable Set Separation in a non-hereditary subclass of perfect graphs. A cut (B,W) of G (a bipartition of V(G)) separates a clique K and a stable set S if $K\subseteq B$ and $S\subseteq W$. A Clique-Stable Set Separator is a family of cuts such that for every clique K, and for every stable set S disjoint from K, there exists a cut in the family that separates K and S. Given a class of graphs, the question is to know whether every graph of the class admits a Clique-Stable Set Separator containing only polynomially many cuts. It is open for the class of all graphs, and also for perfect graphs, which was Yannakakis' original question. Here we investigate on perfect graphs with no balanced skew-partition; the balanced skew-partition was introduced in the proof of the Strong Perfect Graph Theorem. Recently, Chudnovsky, Trotignon, Trunck and Vuskovic proved that forbidding this unfriendly decomposition permits to recursively decompose Berge graphs using 2-join and complement 2-join until reaching a basic graph, and they found an efficient combinatorial algorithm to color those graphs. We apply their decomposition result to prove that perfect graphs with no balanced skew-partition admit a quadratic-size Clique-Stable Set Separator, by taking advantage of the good behavior of 2-join with respect to this property. We then generalize this result and prove that the Strong Erdos-Hajnal property holds in this class, which means that every such graph has a linear-size biclique or complement biclique. This property does not hold for all perfect graphs (Fox 2006), and moreover when the Strong Erdos-Hajnal property holds in a hereditary class of graphs, then both the Erdos-Hajnal property and the polynomial Clique-Stable Set Separation hold.
The Flip Diameter of Rectangulations and Convex Subdivisions
Venue: arXiv cs.DM 2016
Year: 2016

We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of $n$ points. This bound is the best possible for some point sets, while $Θ(n)$ operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of $n$ points in the plane.
Who Watches (and Shares) What on YouTube? And When? Using Twitter to Understand YouTube Viewership
Venue: arXiv cs.SI 2016
Year: 2016

We combine user-centric Twitter data with video-centric YouTube data to analyze who watches and shares what on YouTube. Combination of two data sets, with 87k Twitter users, 5.6mln YouTube videos and 15mln video sharing events, allows rich analysis going beyond what could be obtained with either of the two data sets individually. For Twitter, we generate user features relating to activity, interests and demographics. For YouTube, we obtain video features for topic, popularity and polarization. These two feature sets are combined through sharing events for YouTube URLs on Twitter. This combination is done both in a user-, a video- and a sharing-event-centric manner. For the user-centric analysis, we show how Twitter user features correlate both with YouTube features and with sharing-related features. As two examples, we show urban users are quicker to share than rural users and for some notions of "influence" influential users on Twitter share videos with a higher number of views. For the video-centric analysis, we find a superlinear relation between initial Twitter shares and the final amounts of views, showing the correlated behavior of Twitter. On user impact, we find the total amount of followers of users that shared the video in the first week does not affect its final popularity. However, aggregated user retweet rates serve as a better predictor for YouTube video popularity. For the sharing-centric analysis, we reveal existence of correlated behavior concerning the time between video creation and sharing within certain timescales, showing the time onset for a coherent response, and the time limit after which collective responses are extremely unlikely. We show that response times depend on video category, revealing that Twitter sharing of a video is highly dependent on its content. To the best of our knowledge this is the first large-scale study combining YouTube and Twitter data.