OpenRaiser/Intern-Atlas huggingface dataset:
Efficient Detection of Communities with Significant Overlaps in Networks: Partial Community Merger Algorithm
Venue: arXiv cs.SI 2017
Year: 2017

Detecting communities in large-scale networks is a challenging task when each vertex may belong to multiple communities, as is often the case in social networks. The multiple memberships of vertices and thus the strong overlaps among communities render many detection algorithms invalid. We develop a Partial Community Merger Algorithm (PCMA) for detecting communities with significant overlaps as well as slightly overlapping and disjoint ones. It is a bottom-up approach based on properly reassembling partial information of communities revealed in ego networks of vertices to reconstruct complete communities. Noise control and merger order are the two key issues in implementing this idea. We propose a novel similarity measure between two merged communities that can suppress noise and an efficient algorithm that recursively merges the most similar pair of communities. The validity and accuracy of PCMA is tested against two benchmarks and compared to four existing algorithms. It is the most efficient one with linear complexity and it outperforms the compared algorithms when vertices have multiple memberships. PCMA is applied to two huge online social networks, Friendster and Sina Weibo. Millions of communities are detected and they are of higher qualities than the corresponding metadata groups. We find that the latter should not be regarded as the ground-truth of structural communities. The significant overlapping pattern found in the detected communities confirms the need of new algorithms, such as PCMA, to handle multiple memberships of vertices in social networks.
Safe Controller Optimization for Quadrotors with Gaussian Processes
Venue: arXiv cs.RO 2017
Year: 2017

One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be tuned manually on the real system to achieve the best performance. To avoid this manual tuning step, methods from machine learning, such as Bayesian optimization, have been used. However, as these methods evaluate different controller parameters on the real system, safety-critical system failures may happen. In this paper, we overcome this problem by applying, for the first time, a recently developed safe optimization algorithm, SafeOpt, to the problem of automatic controller parameter tuning. Given an initial, low-performance controller, SafeOpt automatically optimizes the parameters of a control law while guaranteeing safety. It models the underlying performance measure as a Gaussian process and only explores new controller parameters whose performance lies above a safe performance threshold with high probability. Experimental results on a quadrotor vehicle indicate that the proposed method enables fast, automatic, and safe optimization of controller parameters without human intervention.
A commentary on "The now-or-never bottleneck: a fundamental constraint on language", by Christiansen and Chater (2016)
Venue: arXiv cs.CL 2017
Year: 2017

In a recent article, Christiansen and Chater (2016) present a fundamental constraint on language, i.e. a now-or-never bottleneck that arises from our fleeting memory, and explore its implications, e.g., chunk-and-pass processing, outlining a framework that promises to unify different areas of research. Here we explore additional support for this constraint and suggest further connections from quantitative linguistics and information theory.
On the $O_β$-hull of a planar point set
Venue: arXiv cs.CG 2017
Year: 2017

We study the $O_β$-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle $β$. Given a set $P$ of $n$ points in the plane, we show how to maintain the $O_β$-hull of $P$ while $β$ runs from $0$ to $π$ in $O(n \log n)$ time and $O(n)$ space. With the same complexity, we also find the values of $β$ that maximize the area and the perimeter of the $O_β$-hull and, furthermore, we find the value of $β$ achieving the best fitting of the point set $P$ with a two-joint chain of alternate interior angle $β$.
Dynamics at the Boundary of Game Theory and Distributed Computing
Venue: arXiv cs.GT 2017
Year: 2017

We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise in many real-world settings, the participants act as both economic and computational entities. We exhibit a general non-convergence result for a broad class of dynamics in asynchronous settings. We consider implications of our result across a wide variety of interesting and timely applications: game dynamics, circuit design, social networks, Internet routing, and congestion control. We also study the computational and communication complexity of testing the convergence of asynchronous dynamics. Our work opens a new avenue for research at the intersection of distributed computing and game theory.
Algebraic Clustering of Affine Subspaces
Venue: arXiv cs.CV 2017
Year: 2017

Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse representation techniques. While these methods have been applied to both linear and affine subspaces, theoretical results have only been established in the case of linear subspaces. For example, algebraic subspace clustering (ASC) is guaranteed to provide the correct clustering when the data points are in general position and the union of subspaces is transversal. In this paper we study in a rigorous fashion the properties of ASC in the case of affine subspaces. Using notions from algebraic geometry, we prove that the homogenization trick, which embeds points in a union of affine subspaces into points in a union of linear subspaces, preserves the general position of the points and the transversality of the union of subspaces in the embedded space, thus establishing the correctness of ASC for affine subpaces.
Recipes for stable linear embeddings from Hilbert spaces to R^m
Venue: arXiv cs.IT 2017
Year: 2017

We consider the problem of constructing a linear map from a Hilbert space $\mathcal{H}$ (possibly infinite dimensional) to $\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\mathcal{S} \subset \mathcal{H}$. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP on $\mathcal{S}$ with high probability. We also describe a generic technique to construct linear maps that satisfy the RIP. Finally, we detail how to use our results in several examples, which allow us to recover and extend many known compressive sampling results.
An Investigation of Universal Background Sparse Coding Based Speaker Verification on TIMIT
Venue: arXiv cs.SD 2017
Year: 2017

In this paper, we propose a universal background model, named universal background sparse coding (UBSC), for speaker verification. The proposed method trains an ensemble of clusterings by data resampling, and produces sparse codes from the clusterings by one-nearest-neighbor optimization plus binarization. The main advantage of UBSC is that it does not suffer from local minima and does not make Gaussian assumptions on data distributions. We evaluated UBSC on a clean speech corpus---TIMIT. We used the cosine similarity and inner product similarity as the scoring methods of a trial. Experimental results show that UBSC is comparable to Gaussian mixture model.
Multi-Objective Weighted Sampling
Venue: arXiv cs.DB 2017
Year: 2017

{\em Multi-objective samples} are powerful and versatile summaries of large data sets. For a set of keys $x\in X$ and associated values $f_x \geq 0$, a weighted sample taken with respect to $f$ allows us to approximate {\em segment-sum statistics} $\text{Sum}(f;H) = \text{sum}_{x\in H} f_x$, for any subset $H$ of the keys, with statistically-guaranteed quality that depends on sample size and the relative weight of $H$. When estimating $\text{Sum}(g;H)$ for $g\not=f$, however, quality guarantees are lost. A multi-objective sample with respect to a set of functions $F$ provides for each $f\in F$ the same statistical guarantees as a dedicated weighted sample while minimizing the summary size. We analyze properties of multi-objective samples and present sampling schemes and meta-algortithms for estimation and optimization while showcasing two important application domains. The first are key-value data sets, where different functions $f\in F$ applied to the values correspond to different statistics such as moments, thresholds, capping, and sum. A multi-objective sample allows us to approximate all statistics in $F$. The second is metric spaces, where keys are points, and each $f\in F$ is defined by a set of points $C$ with $f_x$ being the service cost of $x$ by $C$, and $\text{Sum}(f;X)$ models centrality or clustering cost of $C$. A multi-objective sample allows us to estimate costs for each $f\in F$. In these domains, multi-objective samples are often of small size, are efficiently to construct, and enable scalable estimation and optimization. We aim here to facilitate further applications of this powerful technique.
A Common Framework for Attitude Synchronization of Unit Vectors in Networks with Switching Topology
Venue: arXiv cs.SY 2017
Year: 2017

In this paper, we study attitude synchronization for elements in the unit sphere of R3 and for elements in the 3D rotation group, for a network with switching topology. The agents angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a given region, unknown to the network. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in R3 as incomplete synchronization, and of 3D rotation matrices as complete synchronization. Our main contribution lies on showing that these two problems can be analyzed under a common framework, where all elements' dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension.
The Impact of Dual Prediction Schemes on the Reduction of the Number of Transmissions in Sensor Networks
Venue: arXiv cs.NI 2017
Year: 2017

Future Internet of Things (IoT) applications will require that billions of wireless devices transmit data to the cloud frequently. However, the wireless medium access is pointed as a problem for the next generations of wireless networks; hence, the number of data transmissions in Wireless Sensor Networks (WSNs) can quickly become a bottleneck, disrupting the exponential growth in the number of interconnected devices, sensors, and amount of produced data. Therefore, keeping a low number of data transmissions is critical to incorporate new sensor nodes and measure a great variety of parameters in future generations of WSNs. Thanks to the high accuracy and low complexity of state-of-the-art forecasting algorithms, Dual Prediction Schemes (DPSs) are potential candidates to optimize the data transmissions in WSNs at the finest level because they facilitate for sensor nodes to avoid unnecessary transmissions without affecting the quality of their measurements. In this work, we present a sensor network model that uses statistical theorems to describe the expected impact of DPSs and data aggregation in WSNs. We aim to provide a foundation for future works by characterizing the theoretical gains of processing data in sensors and conditioning its transmission to the predictions' accuracy. Our simulation results show that the number of transmissions can be reduced by almost 98% in the sensor nodes with the highest workload. We also detail the impact of predicting and aggregating transmissions according to the parameters that can be observed in common scenarios, such as sensor nodes' transmission ranges, the correlation between measurements of different sensors, and the period between two consecutive measurements in a sensor.
Exposing the Probabilistic Causal Structure of Discrimination
Venue: arXiv cs.DB 2017
Year: 2017

Discrimination discovery from data is an important task aiming at identifying patterns of illegal and unethical discriminatory activities against protected-by-law groups, e.g., ethnic minorities. While any legally-valid proof of discrimination requires evidence of causality, the state-of-the-art methods are essentially correlation-based, albeit, as it is well known, correlation does not imply causation. In this paper we take a principled causal approach to the data mining problem of discrimination detection in databases. Following Suppes' probabilistic causation theory, we define a method to extract, from a dataset of historical decision records, the causal structures existing among the attributes in the data. The result is a type of constrained Bayesian network, which we dub Suppes-Bayes Causal Network (SBCN). Next, we develop a toolkit of methods based on random walks on top of the SBCN, addressing different anti-discrimination legal concepts, such as direct and indirect discrimination, group and individual discrimination, genuine requirement, and favoritism. Our experiments on real-world datasets confirm the inferential power of our approach in all these different tasks.
Minimax Lower Bounds for Noisy Matrix Completion Under Sparse Factor Models
Venue: arXiv cs.IT 2017
Year: 2017

This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected per-element squared error for this problem under under several common noise models. Specifically, we analyze scenarios where the corruptions are characterized by additive Gaussian noise or additive heavier-tailed (Laplace) noise, Poisson-distributed observations, and highly-quantized (e.g., one-bit) observations, as instances of our general result. Our results establish that the error bounds derived in (Soni et al., 2016) for complexity-regularized maximum likelihood estimators achieve, up to multiplicative constants and logarithmic factors, the minimax error rates in each of these noise scenarios, provided that the nominal number of observations is large enough, and the sparse factor has (on an average) at least one non-zero per column.
Routing in Unit Disk Graphs
Venue: arXiv cs.CG 2017
Year: 2017

Let $S \subset \mathbb{R}^2$ be a set of $n$ sites. The unit disk graph $\text{UD}(S)$ on $S$ has vertex set $S$ and an edge between two distinct sites $s,t \in S$ if and only if $s$ and $t$ have Euclidean distance $|st| \leq 1$. A routing scheme $R$ for $\text{UD}(S)$ assigns to each site $s \in S$ a label $\ell(s)$ and a routing table $ρ(s)$. For any two sites $s, t \in S$, the scheme $R$ must be able to route a packet from $s$ to $t$ in the following way: given a current site $r$ (initially, $r = s$), a header $h$ (initially empty), and the label $\ell(t)$ of the target, the scheme $R$ consults the routing table $ρ(r)$ to compute a neighbor $r'$ of $r$, a new header $h'$, and the label $\ell(t')$ of an intermediate target $t'$. (The label of the original target may be stored at the header $h'$.) The packet is then routed to $r'$, and the procedure is repeated until the packet reaches $t$. The resulting sequence of sites is called the routing path. The stretch of $R$ is the maximum ratio of the (Euclidean) length of the routing path produced by $R$ and the shortest path in $\text{UD}(S)$, over all pairs of distinct sites in $S$. For any given $\varepsilon > 0$, we show how to construct a routing scheme for $\text{UD}(S)$ with stretch $1+\varepsilon$ using labels of $O(\log n)$ bits and routing tables of $O(\varepsilon^{-5}\log^2 n \log^2 D)$ bits, where $D$ is the (Euclidean) diameter of $\text{UD}(S)$. The header size is $O(\log n \log D)$ bits.
Data compression with low distortion and finite blocklength
Venue: arXiv cs.IT 2017
Year: 2017

This paper considers lossy source coding of $n$-dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $ε$, which is simpler than known dispersion-based approximations. Our approach takes inspiration in the celebrated classical result stating that the Shannon lower bound to rate-distortion function becomes tight in the limit $d \to 0$. We formulate an abstract version of the Shannon lower bound that recovers both the classical Shannon lower bound and the rate-distortion function itself as special cases. Likewise, we show that a nonasymptotic version of the abstract Shannon lower bound recovers all previously known nonasymptotic converses. A necessary and sufficient condition for the Shannon lower bound to be attained exactly is presented. It is demonstrated that whenever that condition is met, the rate-dispersion function is given simply by the varentropy of the source. Remarkably, all finite alphabet sources with balanced distortion measures satisfy that condition in the range of low distortions. Most continuous sources violate that condition. Still, we show that lattice quantizers closely approach the nonasymptotic Shannon lower bound, provided that the source density is smooth enough and the distortion is low. This implies that fine multidimensional lattice coverings are nearly optimal in the rate-distortion sense even at finite $n$. The achievability proof technique is based on a new bound on the output entropy of lattice quantizers in terms of the differential entropy of the source, the lattice cell size and a smoothness parameter of the source density. The technique avoids both the usual random coding argument and the simplifying assumption of the presence of a dither signal.
The packing chromatic number of the infinite square lattice is between 13 and 15
Venue: arXiv cs.DM 2017
Year: 2017

Using a SAT-solver on top of a partial previously-known solution we improve the upper bound of the packing chromatic number of the infinite square lattice from 17 to 15. We discuss the merits of SAT-solving for this kind of problem as well as compare the performance of different encodings. Further, we improve the lower bound from 12 to 13 again using a SAT-solver, demonstrating the versatility of this technology for our approach.
Do Deep Neural Networks Learn Facial Action Units When Doing Expression Recognition?
Venue: arXiv cs.CV 2017
Year: 2017

Despite being the appearance-based classifier of choice in recent years, relatively few works have examined how much convolutional neural networks (CNNs) can improve performance on accepted expression recognition benchmarks and, more importantly, examine what it is they actually learn. In this work, not only do we show that CNNs can achieve strong performance, but we also introduce an approach to decipher which portions of the face influence the CNN's predictions. First, we train a zero-bias CNN on facial expression data and achieve, to our knowledge, state-of-the-art performance on two expression recognition benchmarks: the extended Cohn-Kanade (CK+) dataset and the Toronto Face Dataset (TFD). We then qualitatively analyze the network by visualizing the spatial patterns that maximally excite different neurons in the convolutional layers and show how they resemble Facial Action Units (FAUs). Finally, we use the FAU labels provided in the CK+ dataset to verify that the FAUs observed in our filter visualizations indeed align with the subject's facial movements.
An $O(\log OPT)$-approximation for covering and packing minor models of $θ_r$
Venue: arXiv cs.DS 2017
Year: 2017

Given two graphs $G$ and $H$, we define $\textsf{v-cover}_{H}(G)$ (resp. $\textsf{e-cover}_{H}(G)$) as the minimum number of vertices (resp. edges) whose removal from $G$ produces a graph without any minor isomorphic to ${H}$. Also $\textsf{v-pack}_{H}(G)$ (resp. $\textsf{v-pack}_{H}(G)$) is the maximum number of vertex- (resp. edge-) disjoint subgraphs of $G$ that contain a minor isomaorphic to $H$. We denote by $θ_r$ the graph with two vertices and $r$ parallel edges between them. When $H=θ_r$, the parameters $\textsf{v-cover}_{H}$, $\textsf{e-cover}_{H}$, $\textsf{v-pack}_{H}$, and $\textsf{v-pack}_{H}$ are NP-hard to compute (for sufficiently big values of $r$). Drawing upon combinatorial results in [Minors in graphs of large $θ_r$-girth, Chatzidimitriou et al., arXiv:1510.03041], we give an algorithmic proof that if $\textsf{v-pack}_{θ_r}(G)\leq k$, then $\textsf{v-cover}_{θ_r}(G) = O(k\log k)$, and similarly for $\textsf{v-pack}_{θ_r}$ and $\textsf{e-cover}_{θ_r}$. In other words, the class of graphs containing ${θ_r}$ as a minor has the vertex/edge Erdős-Pósa property, for every positive integer $r$. Using the algorithmic machinery of our proofs, we introduce a unified approach for the design of an $O(\log {\rm OPT})$-approximation algorithm for $\textsf{v-pack}_{θ_r}$, $\textsf{v-cover}_{θ_r}$, $\textsf{v-pack}_{θ_r}$, and $\textsf{e-cover}_{θ_r}$ that runs in $O(n\cdot \log(n)\cdot m)$ steps. Also, we derive several new Erdős-Pósa-type results from the techniques that we introduce.
Distributed Linear Network Operators using Graph Filters
Venue: arXiv cs.IT 2017
Year: 2017

We study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is assumed to be given. Thus, graph-filter design consists in choosing the coefficients of these polynomials (known as filter coefficients) to resemble desired linear transformations. Due to the local structure of the graph-shift operator, graph filters can be implemented distributedly across nodes, making them suitable for networked settings. We determine spectral conditions under which a specific linear transformation can be implemented perfectly using graph filters. Furthermore, for the cases where perfect implementation is infeasible, the design of optimal approximations for different error metrics is analyzed. We introduce the notion of a node-variant graph filter, which allows the simultaneous implementation of multiple (regular) graph filters in different nodes of the graph. This additional flexibility enables the design of more general operators without undermining the locality in implementation. Perfect and approximate implementation of network operators is also studied for node-variant graph filters. We demonstrate the practical relevance of the developed framework by studying in detail the application of graph filters to the problems of finite-time consensus and analog network coding. Finally, we present additional numerical experiments comparing the performance of node-invariant and node-variant filters when approximating arbitrary linear network operators.