OpenRaiser/Intern-Atlas huggingface dataset:
Upper Bounding the Graph Edit Distance Based on Rings and Machine Learning
Venue: arXiv cs.DS 2021
Year: 2021

The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is NP-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via transformations to the linear sum assignment problem with error-correction (LSAPE). Typically, local structures and distances between them are employed for carrying out this transformation, but recently also machine learning techniques have been used. In this paper, we formally define a unifying framework LSAPE-GED for transformations from GED to LSAPE. We also introduce rings, a new kind of local structures designed for graphs where most information resides in the topology rather than in the node labels. Furthermore, we propose two new ring based heuristics RING and RING-ML, which instantiate LSAPE-GED using the traditional and the machine learning based approach for transforming GED to LSAPE, respectively. Extensive experiments show that using rings for upper bounding GED significantly improves the state of the art on datasets where most information resides in the graphs' topologies. This closes the gap between fast but rather inaccurate LSAPE based heuristics and more accurate but significantly slower GED algorithms based on local search.
Nonstationary Gauss-Markov Processes: Parameter Estimation and Dispersion
Venue: arXiv cs.IT 2021
Year: 2021

This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1} + Z_i,~i\geq 1$, where $U_0 = 0$, $a> 1$, and $Z_i$'s are independent Gaussian random variables with zero mean and variance $σ^2$. We show a tight nonasymptotic exponentially decaying bound on the tail probability of the estimation error. Unlike previous works, our bound is tight already for a sample size of the order of hundreds. We apply the new estimation bound to find the dispersion for lossy compression of nonstationary Gauss-Markov sources. We show that the dispersion is given by the same integral formula that we derived previously for the asymptotically stationary Gauss-Markov sources, i.e., $|a| < 1$. New ideas in the nonstationary case include separately bounding the maximum eigenvalue (which scales exponentially) and the other eigenvalues (which are bounded by constants that depend only on $a$) of the covariance matrix of the source sequence, and new techniques in the derivation of our estimation error bound.
The Complexity of Approximately Counting Retractions to Square-Free Graphs
Venue: arXiv cs.CC 2021
Year: 2021

A retraction is a homomorphism from a graph $G$ to an induced subgraph $H$ of $G$ that is the identity on $H$. In a long line of research, retractions have been studied under various algorithmic settings. Recently, the problem of approximately counting retractions was considered. We give a complete trichotomy for the complexity of approximately counting retractions to all square-free graphs (graphs that do not contain a cycle of length $4$). It turns out there is a rich and interesting class of graphs for which this problem is complete in the class $\#\mathrm{BIS}$. As retractions generalise homomorphisms, our easiness results extend to the important problem of approximately counting homomorphisms. By giving new $\#\mathrm{BIS}$-easiness results we now settle the complexity of approximately counting homomorphisms for a whole class of non-trivial graphs which were previously unresolved.
Energy of Computing on Multicore CPUs: Predictive Models and Energy Conservation Law
Venue: arXiv cs.DC 2021
Year: 2021

Energy is now a first-class design constraint along with performance in all computing settings. Energy predictive modelling based on performance monitoring counts (PMCs) is the leading method used for prediction of energy consumption during an application execution. We use a model-theoretic approach to formulate the assumed properties of existing models in a mathematical form. We extend the formalism by adding properties, heretofore unconsidered, that account for a limited form of energy conservation law. The extended formalism defines our theory of energy of computing. By applying the basic practical implications of the theory, we improve the prediction accuracy of state-of-the-art energy models from 31% to 18%. We also demonstrate that use of state-of-the-art measurement tools for energy optimisation may lead to significant losses of energy (ranging from 56% to 65% for applications used in experiments) since they do not take into account the energy conservation properties.
Hitting minors on bounded treewidth graphs. IV. An optimal algorithm
Venue: arXiv cs.DS 2021
Year: 2021

For a fixed finite collection of graphs ${\cal F}$, the ${\cal F}$-M-DELETION problem asks, given an $n$-vertex input graph $G,$ for the minimum number of vertices that intersect all minor models in $G$ of the graphs in ${\cal F}$. by Courcelle Theorem, this problem can be solved in time $f_{\cal F}(tw)\cdot n^{O(1)},$ where $tw$ is the treewidth of $G$, for some function $f_{\cal F}$ depending on ${\cal F}$ In a recent series of articles, we have initiated the programme of optimizing asymptotically the function $f_{\cal F}$. Here we provide an algorithm showing that $f_{\cal F}(tw) = 2^{O(tw\cdot \log tw)}$ for every collection ${\cal F}$. Prior to this work, the best known function $f_{\cal F}$ was double-exponential in $tw$. In particular, our algorithm vastly extends the results of Jansen et al. [SODA 2014] for the particular case ${\cal F}=\{K_5,K_{3,3}\}$ and of Kociumaka and Pilipczuk [Algorithmica 2019] for graphs of bounded genus, and answers an open problem posed by Cygan et al. [Inf Comput 2017]. We combine several ingredients such as the machinery of boundaried graphs in dynamic programming via representatives, the Flat Wall Theorem, Bidimensionality, the irrelevant vertex technique, treewidth modulators, and protrusion replacement. Together with our previous results providing single-exponential algorithms for particular collections ${\cal F}$ [Theor Comput Sci 2020] and general lower bounds [J Comput Syst Sci 2020], our algorithm yields the following complexity dichotomy when ${\cal F} = \{H\}$ contains a single connected graph $H,$ assuming the Exponential Time Hypothesis: $f_H(tw)=2^{Θ(tw)}$ if $H$ is a contraction of the chair or the banner, and $f_H(tw)=2^{Θ(tw\cdot \log tw)}$ otherwise.
Active Rendezvous for Multi-Robot Pose Graph Optimization using Sensing over Wi-Fi
Venue: arXiv cs.RO 2021
Year: 2021

We present a novel framework for collaboration amongst a team of robots performing Pose Graph Optimization (PGO) that addresses two important challenges for multi-robot SLAM: i) that of enabling information exchange "on-demand" via Active Rendezvous without using a map or the robot's location, and ii) that of rejecting outlying measurements. Our key insight is to exploit relative position data present in the communication channel between robots to improve groundtruth accuracy of PGO. We develop an algorithmic and experimental framework for integrating Channel State Information (CSI) with multi-robot PGO; it is distributed, and applicable in low-lighting or featureless environments where traditional sensors often fail. We present extensive experimental results on actual robots and observe that using Active Rendezvous results in a 64% reduction in ground truth pose error and that using CSI observations to aid outlier rejection reduces ground truth pose error by 32%. These results show the potential of integrating communication as a novel sensor for SLAM.
Deep Metric Learning with Alternating Projections onto Feasible Sets
Venue: arXiv cs.CV 2021
Year: 2021

During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance metric learning problem as finding a feasible point of a constraint set where the embedding vectors of the training data satisfy desired intra-class and inter-class proximity. The feasible set induced by the constraint set is expressed as the intersection of the relaxed feasible sets which enforce the proximity constraints only for particular samples (a sample from each class) of the training data. Then, the feasible point problem is to be approximately solved by performing alternating projections onto those feasible sets. Such an approach introduces a regularization term and results in minimizing a typical loss function with a systematic batch set construction where these batches are constrained to contain the same sample from each class for a certain number of iterations. Moreover, these particular samples can be considered as the class representatives, allowing efficient utilization of hard class mining during batch construction. The proposed technique is applied with the well-accepted losses and evaluated on Stanford Online Products, CAR196 and CUB200-2011 datasets for image retrieval and clustering. Outperforming state-of-the-art, the proposed approach consistently improves the performance of the integrated loss functions with no additional computational cost and boosts the performance further by hard negative class mining.
TED-On: A Total Error Framework for Digital Traces of Human Behavior on Online Platforms
Venue: arXiv cs.CY 2021
Year: 2021

Peoples' activities and opinions recorded as digital traces online, especially on social media and other web-based platforms, offer increasingly informative pictures of the public. They promise to allow inferences about populations beyond the users of the platforms on which the traces are recorded, representing real potential for the Social Sciences and a complement to survey-based research. But the use of digital traces brings its own complexities and new error sources to the research enterprise. Recently, researchers have begun to discuss the errors that can occur when digital traces are used to learn about humans and social phenomena. This article synthesizes this discussion and proposes a systematic way to categorize potential errors, inspired by the Total Survey Error (TSE) Framework developed for survey methodology. We introduce a conceptual framework to diagnose, understand, and document errors that may occur in studies based on such digital traces. While there are clear parallels to the well-known error sources in the TSE framework, the new "Total Error Framework for Digital Traces of Human Behavior on Online Platforms" (TED-On) identifies several types of error that are specific to the use of digital traces. By providing a standard vocabulary to describe these errors, the proposed framework is intended to advance communication and research concerning the use of digital traces in scientific social research.
Automatic crack classification by exploiting statistical event descriptors for Deep Learning
Venue: arXiv cs.LG 2021
Year: 2021

In modern building infrastructures, the chance to devise adaptive and unsupervised data-driven health monitoring systems is gaining in popularity due to the large availability of big data from low-cost sensors with communication capabilities and advanced modeling tools such as Deep Learning. The main purpose of this paper is to combine deep neural networks with Bidirectional Long Short Term Memory and advanced statistical analysis involving Instantaneous Frequency and Spectral Kurtosis to develop an accurate classification tool for tensile, shear and mixed modes originated from acoustic emission events (cracks). We investigated on effective event descriptors to capture the unique characteristics from the different types of modes. Tests on experimental results confirm that this method achieves promising classification among different crack events and can impact on the design of future on structural health monitoring (SHM) technologies. This approach is effective to classify incipient damages with 92% of accuracy, which is advantageous to plan maintenance.
Exponential Slowdown for Larger Populations: The $(μ+1)$-EA on Monotone Functions
Venue: arXiv cs.NE 2021
Year: 2021

Pseudo-Boolean monotone functions are unimodal functions which are trivial to optimize for some hillclimbers, but are challenging for a surprising number of evolutionary algorithms (EAs). A general trend is that EAs are efficient if parameters like the mutation rate are set conservatively, but may need exponential time otherwise. In particular, it was known that the $(1+1)$-EA and the $(1+λ)$-EA can optimize every monotone function in pseudolinear time if the mutation rate is $c/n$ for some $c<1$, but they need exponential time for some monotone functions for $c>2.2$. The second part of the statement was also known for the $(μ+1)$-EA. In this paper we show that the first statement does not apply to the $(μ+1)$-EA. More precisely, we prove that for every constant $c>0$ there is a constant integer $μ_0$ such that the $(μ+1)$-EA with mutation rate $c/n$ and population size $μ_0\leμ\le n$ needs superpolynomial time to optimize some monotone functions. Thus, increasing the population size by just a constant has devastating effects on the performance. This is in stark contrast to many other benchmark functions on which increasing the population size either increases the performance significantly, or affects performance mildly. The reason why larger populations are harmful lies in the fact that larger populations may temporarily decrease selective pressure on parts of the population. This allows unfavorable mutations to accumulate in single individuals and their descendants. If the population moves sufficiently fast through the search space, such unfavorable descendants can become ancestors of future generations, and the bad mutations are preserved. Remarkably, this effect only occurs if the population renews itself sufficiently fast, which can only happen far away from the optimum. This is counter-intuitive since usually optimization gets harder as we approach the optimum.
Min-max Entropy for Weakly Supervised Pointwise Localization
Venue: arXiv cs.CV 2021
Year: 2021

Pointwise localization allows more precise localization and accurate interpretability, compared to bounding box, in applications where objects are highly unstructured such as in medical domain. In this work, we focus on weakly supervised localization (WSL) where a model is trained to classify an image and localize regions of interest at pixel-level using only global image annotation. Typical convolutional attentions maps are prune to high false positive regions. To alleviate this issue, we propose a new deep learning method for WSL, composed of a localizer and a classifier, where the localizer is constrained to determine relevant and irrelevant regions using conditional entropy (CE) with the aim to reduce false positive regions. Experimental results on a public medical dataset and two natural datasets, using Dice index, show that, compared to state of the art WSL methods, our proposal can provide significant improvements in terms of image-level classification and pixel-level localization (low false positive) with robustness to overfitting. A public reproducible PyTorch implementation is provided in: https://github.com/sbelharbi/wsol-min-max-entropy-interpretability .
FLUID: A Common Model for Semantic Structural Graph Summaries Based on Equivalence Relations
Venue: arXiv cs.DB 2021
Year: 2021

Summarization is a widespread method for handling very large graphs. The task of structural graph summarization is to compute a concise but meaningful synopsis of the key structural information of a graph. As summaries may be used for many different purposes, there is no single concept or model of graph summaries. We have studied existing structural graph summaries for large-scale (semantic) graphs. Despite their different concepts and purposes, we found commonalities in the graph structures they capture. We use these commonalities to provide for the first time a formally defined common model, FLUID (FLexible graph sUmmarIes for Data graphs), that allows us to flexibly define structural graph summaries. FLUID allows graph summaries to be quickly defined, adapted, and compared for different purposes and datasets. To this end, FLUID provides features of structural summarization based on equivalence relations such as distinction of types and properties, direction of edges, bisimulation, and inference. We conduct a detailed complexity analysis of the features provided by FLUID. We show that graph summaries defined with FLUID can be computed in the worst case in time $\mathcal{O}(n^2)$ w.r.t. $n$, the number of edges in the data graph. An empirical analysis of large-scale web graphs with billions of edges indicates a typical running time of $Θ(n)$. Based on the formal FLUID model, one can quickly define and modify various structural graph summaries from the literature and beyond.
Solving high-dimensional optimal stopping problems using deep learning
Venue: arXiv cs.CE 2021
Year: 2021

Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number of underlying assets. High-dimensional optimal stopping problems are, however, notoriously difficult to solve due to the well-known curse of dimensionality. In this work, we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option. The proposed algorithm can also be applied to optimal stopping problems that arise in other areas where the underlying stochastic process can be efficiently simulated. We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options, such as Bermudan max-call options in up to 5000 dimensions. Most of the obtained results are compared to reference values computed by exploiting the specific problem design or, where available, to reference values from the literature. These numerical results suggest that the proposed algorithm is highly effective in the case of many underlyings, in terms of both accuracy and speed.
Logic could be learned from images
Venue: arXiv cs.CV 2021
Year: 2021

Logic reasoning is a significant ability of human intelligence and also an important task in artificial intelligence. The existing logic reasoning methods, quite often, need to design some reasoning patterns beforehand. This has led to an interesting question: can logic reasoning patterns be directly learned from given data? The problem is termed as a data concept logic. In this study, a learning logic task from images, called a LiLi task, first is proposed. This task is to learn and reason the logic relation from images, without presetting any reasoning patterns. As a preliminary exploration, we design six LiLi data sets (Bitwise And, Bitwise Or, Bitwise Xor, Addition, Subtraction and Multiplication), in which each image is embedded with a n-digit number. It is worth noting that a learning model beforehand does not know the meaning of the n-digit numbers embedded in images and the relation between the input images and the output image. In order to tackle the task, in this work we use many typical neural network models and produce fruitful results. However, these models have the poor performances on the difficult logic task. For furthermore addressing this task, a novel network framework called a divide and conquer model by adding some label information is designed, achieving a high testing accuracy.
Bayesian Incremental Inference Update by Re-using Calculations from Belief Space Planning: A New Paradigm
Venue: arXiv cs.AI 2021
Year: 2021

Inference and decision making under uncertainty are key processes in every autonomous system and numerous robotic problems. In recent years, the similarities between inference and decision making triggered much work, from developing unified computational frameworks to pondering about the duality between the two. In spite of these efforts, inference and control, as well as inference and belief space planning (BSP) are still treated as two separate processes. In this paper we propose a paradigm shift, a novel approach which deviates from conventional Bayesian inference and utilizes the similarities between inference and BSP. We make the key observation that inference can be efficiently updated using predictions made during the decision making stage, even in light of inconsistent data association between the two. We developed a two staged process that implements our novel approach and updates inference using calculations from the precursory planning phase. Using autonomous navigation in an unknown environment along with iSAM2 efficient methodologies as a test case, we benchmarked our novel approach against standard Bayesian inference, both with synthetic and real-world data (KITTI dataset). Results indicate that not only our approach improves running time by at least a factor of two while providing the same estimation accuracy, but it also alleviates the computational burden of state dimensionality and loop closures.
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization
Venue: arXiv cs.IT 2021
Year: 2021

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction to an augmented single-penalty formulation, to the non-convex setting and discuss its computational intractability in large-scale applications. To circumvent this limitation, we propose an alternative single-penalty reduction based on infimal convolution that shares the benefits of the augmented approach but is computationally less dependent on the problem size. We provide linear convergence rates for both approaches, and their dependence on design parameters. Numerical experiments substantiate our theoretical findings.