OpenRaiser/Intern-Atlas huggingface dataset:
A faster method for computing Gama-Nguyen-Regev's extreme pruning coefficients
Venue: arXiv cs.CR 2018
Year: 2018

This paper considers Gama-Nguyen-Regev's strategy [GNR10] for optimizing pruning coefficients for lattice vector enumeration. We give a table of optimized coefficients and proposes a faster method for computing near-optimized coefficients for any parameters by interpolation. From the first version published in 2014, we inserted new Section 3.3 to introduce our recent technique to compute approximations of enumeration cost and success probability; both are completed in O(n^2) floating point operations where n is the lattice dimension. For readers who are interested in this topic, we keep the descriptions of our heuristic optimization method in Section 4 although they are outdated now.
A note on multipivot Quicksort
Venue: arXiv cs.DS 2018
Year: 2018

We analyse a generalisation of the Quicksort algorithm, where k uniformly at random chosen pivots are used for partitioning an array of n distinct keys. Specifically, the expected cost of this scheme is obtained, under the assumption of linearity of the cost needed for the partition process. The integration constants of the expected cost are computed using Vandermonde matrices.
Multilayer bootstrap networks
Venue: arXiv cs.LG 2018
Year: 2018

Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected features as its centroids, and learns a one-hot encoder by one-nearest-neighbor optimization. Geometrically, the nonparametric density estimator at each layer projects the input data space to a uniformly-distributed discrete feature space, where the similarity of two data points in the discrete feature space is measured by the number of the nearest centroids they share in common. The multilayer network gradually reduces the nonlinear variations of data from bottom up by building a vast number of hierarchical trees implicitly on the original data space. Theoretically, the estimation error caused by the nonparametric density estimator is proportional to the correlation between the clusterings, both of which are reduced by the randomization steps.
Stable Cosparse Recovery via \ell_p-analysis Optimization
Venue: arXiv cs.IT 2018
Year: 2018

In this paper we study the $\ell_p$-analysis optimization ($0<p\leq1$) problem for cosparse signal recovery. We establish a bound for recovery error via the restricted $p$-isometry property over any subspace. We further prove that the nonconvex $\ell_q$-analysis optimization can do recovery with a lower sample complexity and in a wider range of cosparsity than its convex counterpart. In addition, we develop an iteratively reweighted method to solve the optimization problem under a variational framework. Empirical results of preliminary computational experiments illustrate that the nonconvex method outperforms its convex counterpart.
Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks
Venue: arXiv cs.CR 2018
Year: 2018

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.
On the Inequalities of Projected Volumes and the Constructible Region
Venue: arXiv cs.DM 2018
Year: 2018

We study the following geometry problem: given a $2^n-1$ dimensional vector $π=\{π_S\}_{S\subseteq [n], S\ne \emptyset}$, is there an object $T\subseteq\mathbb{R}^n$ such that $\log(\mathsf{vol}(T_S))= π_S$, for all $S\subseteq [n]$, where $T_S$ is the projection of $T$ to the subspace spanned by the axes in $S$? If $π$ does correspond to an object in $\mathbb{R}^n$, we say that $π$ is {\em constructible}. We use $Ψ_n$ to denote the constructible region, i.e., the set of all constructible vectors in $\mathbb{R}^{2^n-1}$. In 1995, Bollobás and Thomason showed that $Ψ_n$ is contained in a polyhedral cone, defined a class of so called uniform cover inequalities. We propose a new set of natural inequalities, called nonuniform-cover inequalities, which generalize the BT inequalities. We show that any linear inequality that all points in $Ψ_n$ satisfy must be a nonuniform-cover inequality. Based on this result and an example by Bollobás and Thomason, we show that constructible region $Ψ_n$ is not even convex, and thus cannot be fully characterized by linear inequalities. We further show that some subclasses of the nonuniform-cover inequalities are not correct by various combinatorial constructions, which refutes a previous conjecture about $Ψ_n$. Finally, we conclude with an interesting conjecture regarding the convex hull of $Ψ_n$.
Computational Aspects of the Colorful Carathéodory Theorem
Venue: arXiv cs.CG 2018
Year: 2018

Let $C_1,\dots,C_{d+1}\subset \mathbb{R}^d$ be $d+1$ point sets, each containing the origin in its convex hull. We call these sets color classes, and we call a sequence $p_1, \dots, p_{d+1}$ with $p_i \in C_i$, for $i = 1, \dots, d+1$, a colorful choice. The colorful Carathéodory theorem guarantees the existence of a colorful choice that also contains the origin in its convex hull. The computational complexity of finding such a colorful choice (CCP) is unknown. This is particularly interesting in the light of polynomial-time reductions from several related problems, such as computing centerpoints, to CCP. We define a novel notion of approximation that is compatible with the polynomial-time reductions to CCP: a sequence that contains at most $k$ points from each color class is called a $k$-colorful choice. We present an algorithm that for any fixed $\varepsilon > 0$, outputs an $\lceil εd\rceil$-colorful choice containing the origin in its convex hull in polynomial time. Furthermore, we consider a related problem of CCP: in the nearest colorful polytope problem (NCP), we are given sets $C_1,\dots,C_n\subset\mathbb{R}^d$ that do not necessarily contain the origin in their convex hulls. The goal is to find a colorful choice whose convex hull minimizes the distance to the origin. We show that computing a local optimum for NCP is PLS-complete, while computing a global optimum is NP-hard.
Deducing Truth from Correlation
Venue: arXiv cs.IT 2018
Year: 2018

This work is motivated by a question at the heart of unsupervised learning approaches: Assume we are collecting a number K of (subjective) opinions about some event E from K different agents. Can we infer E from them? Prima facie this seems impossible, since the agents may be lying. We model this task by letting the events be distributed according to some distribution p and the task is to estimate p under unknown noise. Again, this is impossible without additional assumptions. We report here the finding of very natural such assumptions - the availability of multiple copies of the true data, each under independent and invertible (in the sense of matrices) noise, is already sufficient: If the true distribution and the observations are modeled on the same finite alphabet, then the number of such copies needed to determine p to the highest possible precision is exactly three! This result can be seen as a counterpart to independent component analysis. Therefore, we call our approach 'dependent component analysis'. In addition, we present generalizations of the model to different alphabet sizes at in- and output. A second result is found: the 'activation' of invertibility through multiple parallel uses.
Sub-linear Time Support Recovery for Compressed Sensing using Sparse-Graph Codes
Venue: arXiv cs.IT 2018
Year: 2018

We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key contribution is a new compressed sensing framework through a new family of carefully designed sparse measurement matrices associated with minimal measurement costs and a low-complexity recovery algorithm. The measurement matrix in our framework is designed based on the well-crafted sparsification through capacity-approaching sparse-graph codes, where the sparse coefficients can be recovered efficiently in a few iterations by performing simple error decoding over the observations. We formally connect this general recovery problem with sparse-graph decoding in packet communication systems, and analyze our framework in terms of the measurement cost, time complexity and recovery performance. In the noiseless setting, our framework can recover any arbitrary $K$-sparse signal in $O(K)$ time using $2K$ measurements asymptotically with high probability. In the noisy setting, when the sparse coefficients take values in a finite and quantized alphabet, our framework can achieve the same goal in time $O(K\log(N/K))$ using $O(K\log(N/K))$ measurements obtained from measurement matrix with elements $\{-1,0,1\}$. When the sparsity $K$ is sub-linear in the signal dimension $K=O(N^δ)$ for some $0<δ<1$, our results are order-optimal in terms of measurement costs and run-time, both of which are sub-linear in the signal dimension $N$. The sub-linear measurement cost and run-time can also be achieved with continuous-valued sparse coefficients, with a slight increment in the logarithmic factors. This offers the desired scalability of our framework that can potentially enable real-time or near-real-time processing for massive datasets featuring sparsity.
Clustering based on the In-tree Graph Structure and Affinity Propagation
Venue: arXiv cs.LG 2018
Year: 2018

A recently proposed clustering method, called the Nearest Descent (ND), can organize the whole dataset into a sparsely connected graph, called the In-tree. This ND-based Intree structure proves able to reveal the clustering structure underlying the dataset, except one imperfect place, that is, there are some undesired edges in this In-tree which require to be removed. Here, we propose an effective way to automatically remove the undesired edges in In-tree via an effective combination of the In-tree structure with affinity propagation (AP). The key for the combination is to add edges between the reachable nodes in In-tree before using AP to remove the undesired edges. The experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed method.
A speed and departure time optimization algorithm for the Pollution-Routing Problem
Venue: arXiv cs.DS 2018
Year: 2018

We propose a new speed and departure time optimization algorithm for the Pollution-Routing Problem (PRP), which runs in quadratic time and returns a certified optimal schedule. This algorithm is embedded into an iterated local search-based metaheuristic to achieve a combined speed, scheduling and routing optimization. The start of the working day is set as a decision variable for individual routes, thus enabling a better assignment of human resources to required demands. Some routes that were evaluated as unprofitable can now appear as viable candidates later in the day, leading to a larger search space and further opportunities of distance optimization via better service consolidation. Extensive computational experiments on available PRP benchmark instances demonstrate the good performance of the algorithms. The flexible departure times from the depot contribute to reduce the operational costs by 8.36% on the considered instances.
Compressive Sampling of Ensembles of Correlated Signals
Venue: arXiv cs.IT 2018
Year: 2018

We propose several sampling architectures for the efficient acquisition of an ensemble of correlated signals. We show that without prior knowledge of the correlation structure, each of our architectures (under different sets of assumptions) can acquire the ensemble at a sub-Nyquist rate. Prior to sampling, the analog signals are diversified using simple, implementable components. The diversification is achieved by injecting types of "structured randomness" into the ensemble, the result of which is subsampled. For reconstruction, the ensemble is modeled as a low-rank matrix that we have observed through an (undetermined) set of linear equations. Our main results show that this matrix can be recovered using standard convex programming techniques when the total number of samples is on the order of the intrinsic degree of freedom of the ensemble --- the more heavily correlated the ensemble, the fewer samples are needed. To motivate this study, we discuss how such ensembles arise in the context of array processing.
Rigorous Deductive Argumentation for Socially Relevant Issues
Venue: arXiv cs.LO 2018
Year: 2018

The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial, rigorous deductive arguments concerning such problems -without eliminating the complications of vagueness, subjectivity, and uncertainty- is, though very difficult, not problematic in principle, does not require the invention of new logics -classical first-order logic will do- and is something that more mathematically-inclined people should be pursuing. The framework of interpreted formal proofs is presented for formalizing and criticizing rigorous deductive arguments about vague, subjective, and uncertain issues, and its adequacy is supported largely by a number of major examples. This thesis also documents progress towards a web system for collaboratively authoring and criticizing such arguments, which is the ultimate goal of this project.
Highly corrupted image inpainting through hypoelliptic diffusion
Venue: arXiv cs.CV 2018
Year: 2018

We present a new image inpainting algorithm, the Averaging and Hypoelliptic Evolution (AHE) algorithm, inspired by the one presented in [SIAM J. Imaging Sci., vol. 7, no. 2, pp. 669--695, 2014] and based upon a semi-discrete variation of the Citti-Petitot-Sarti model of the primary visual cortex V1. The AHE algorithm is based on a suitable combination of sub-Riemannian hypoelliptic diffusion and ad-hoc local averaging techniques. In particular, we focus on reconstructing highly corrupted images (i.e. where more than the 80% of the image is missing), for which we obtain reconstructions comparable with the state-of-the-art.
Mean Field Games in Nudge Systems for Societal Networks
Venue: arXiv cs.GT 2018
Year: 2018

We consider the general problem of resource sharing in societal networks, consisting of interconnected communication, transportation, energy and other networks important to the functioning of society. Participants in such network need to take decisions daily, both on the quantity of resources to use as well as the periods of usage. With this in mind, we discuss the problem of incentivizing users to behave in such a way that society as a whole benefits. In order to perceive societal level impact, such incentives may take the form of rewarding users with lottery tickets based on good behavior, and periodically conducting a lottery to translate these tickets into real rewards. We will pose the user decision problem as a mean field game (MFG), and the incentives question as one of trying to select a good mean field equilibrium (MFE). In such a framework, each agent (a participant in the societal network) takes a decision based on an assumed distribution of actions of his/her competitors, and the incentives provided by the social planner. The system is said to be at MFE if the agent's action is a sample drawn from the assumed distribution. We will show the existence of such an MFE under different settings, and also illustrate how to choose an attractive equilibrium using as an example demand-response in energy networks.
Towards Easier and Faster Sequence Labeling for Natural Language Processing: A Search-based Probabilistic Online Learning Framework (SAPO)
Venue: arXiv cs.LG 2018
Year: 2018

There are two major approaches for sequence labeling. One is the probabilistic gradient-based methods such as conditional random fields (CRF) and neural networks (e.g., RNN), which have high accuracy but drawbacks: slow training, and no support of search-based optimization (which is important in many cases). The other is the search-based learning methods such as structured perceptron and margin infused relaxed algorithm (MIRA), which have fast training but also drawbacks: low accuracy, no probabilistic information, and non-convergence in real-world tasks. We propose a novel and "easy" solution, a search-based probabilistic online learning method, to address most of those issues. The method is "easy", because the optimization algorithm at the training stage is as simple as the decoding algorithm at the test stage. This method searches the output candidates, derives probabilities, and conducts efficient online learning. We show that this method with fast training and theoretical guarantee of convergence, which is easy to implement, can support search-based optimization and obtain top accuracy. Experiments on well-known tasks show that our method has better accuracy than CRF and BiLSTM\footnote{The SAPO code is released at \url{https://github.com/lancopku/SAPO}.}.
A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths
Venue: arXiv cs.DC 2018
Year: 2018

We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here $n$ is the number of nodes in the network and $D$ is its (hop) diameter. This is the first non-trivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized $(1+o(1))$-approximation $\tilde O(n^{1/2}D^{1/4}+D)$-time algorithm of Nanongkai [STOC 2014] by a factor of as large as $n^{1/8}$, and (ii) the $O(ε^{-1}\log ε^{-1})$-approximation factor of Lenzen and Patt-Shamir's $\tilde O(n^{1/2+ε}+D)$-time algorithm [STOC 2013] within the same running time. Our running time matches the known time lower bound of $Ω(n^{1/2}/\log n + D)$ [Elkin STOC 2004] up to subpolynomial factors, thus essentially settling the status of this problem which was raised at least a decade ago [Elkin SIGACT News 2004]. It also implies a $(2+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [OPODIS 2015]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the "hitting set argument" commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic, construction of an $(n^{o(1)}, o(1))$-hop set of size $n^{1+o(1)}$. We combine these techniques with many distributed algorithmic techniques, some of which from problems that are not directly related to shortest paths, e.g., ruling sets [Goldberg et al. STOC 1987], source detection [Lenzen and Peleg PODC 2013], and partial distance estimation [Lenzen and Patt-Shamir PODC 2015].
Multi-Target Tracking in Distributed Sensor Networks using Particle PHD Filters
Venue: arXiv cs.MA 2018
Year: 2018

Multi-target tracking is an important problem in civilian and military applications. This paper investigates multi-target tracking in distributed sensor networks. Data association, which arises particularly in multi-object scenarios, can be tackled by various solutions. We consider sequential Monte Carlo implementations of the Probability Hypothesis Density (PHD) filter based on random finite sets. This approach circumvents the data association issue by jointly estimating all targets in the region of interest. To this end, we develop the Diffusion Particle PHD Filter (D-PPHDF) as well as a centralized version, called the Multi-Sensor Particle PHD Filter (MS-PPHDF). Their performance is evaluated in terms of the Optimal Subpattern Assignment (OSPA) metric, benchmarked against a distributed extension of the Posterior Cramér-Rao Lower Bound (PCRLB), and compared to the performance of an existing distributed PHD Particle Filter. Furthermore, the robustness of the proposed tracking algorithms against outliers and their performance with respect to different amounts of clutter is investigated.
How Far Can You Get By Combining Change Detection Algorithms?
Venue: arXiv cs.CV 2018
Year: 2018

Given the existence of many change detection algorithms, each with its own peculiarities and strengths, we propose a combination strategy, that we termed IUTIS (In Unity There Is Strength), based on a genetic Programming framework. This combination strategy is aimed at leveraging the strengths of the algorithms and compensate for their weakness. In this paper we show our findings in applying the proposed strategy in two different scenarios. The first scenario is purely performance-based. The second scenario performance and efficiency must be balanced. Results demonstrate that starting from simple algorithms we can achieve comparable results with respect to more complex state-of-the-art change detection algorithms, while keeping the computational complexity affordable for real-time applications.
Pinball Loss Minimization for One-bit Compressive Sensing: Convex Models and Algorithms
Venue: arXiv cs.IT 2018
Year: 2018

The one-bit quantization is implemented by one single comparator that operates at low power and a high rate. Hence one-bit compressive sensing (1bit-CS) becomes attractive in signal processing. When measurements are corrupted by noise during signal acquisition and transmission, 1bit-CS is usually modeled as minimizing a loss function with a sparsity constraint. The one-sided $\ell_1$ loss and the linear loss are two popular loss functions for 1bit-CS. To improve the decoding performance on noisy data, we consider the pinball loss, which provides a bridge between the one-sided $\ell_1$ loss and the linear loss. Using the pinball loss, two convex models, an elastic-net pinball model and its modification with the $\ell_1$-norm constraint, are proposed. To efficiently solve them, the corresponding dual coordinate ascent algorithms are designed and their convergence is proved. The numerical experiments confirm the effectiveness of the proposed algorithms and the performance of the pinball loss minimization for 1bit-CS.