arXiv subjects

Rik Sarkar

Publications and source records attributed to Rik Sarkar.

35 records · Page 2Linked to original sources

arXiv2022

On Cyclic Solutions to the Min-Max Latency Multi-Robot Patrolling Problem

We consider the following surveillance problem: Given a set $P$ of $n$ sites in a metric space and a set of $k$ robots with the same maximum speed, compute a patrol schedule of minimum latency for the robots. Here a patrol schedule specifies for each robot an infinite sequence of sites to visit (in the given order) and the latency $L$ of a schedule is the maximum latency of any site, where the latency of a site $s$ is the supremum of the lengths of the time intervals between consecutive visits to $s$. When $k=1$ the problem is equivalent to the travelling salesman problem (TSP) and thus it is NP-hard. We have two main results. We consider cyclic solutions in which the set of sites must be partitioned into $\ell$ groups, for some~$\ell \leq k$, and each group is assigned a subset of the robots that move along the travelling salesman tour of the group at equal distance from each other. Our first main result is that approximating the optimal latency of the class of cyclic solutions can be reduced to approximating the optimal travelling salesman tour on some input, with only a $1+\varepsilon$ factor loss in the approximation factor and an $O\left(\left( k/\varepsilon \right)^k\right)$ factor loss in the runtime, for any $\varepsilon >0$. Our second main result shows that an optimal cyclic solution is a $2(1-1/k)$-approximation of the overall optimal solution. Note that for $k=2$ this implies that an optimal cyclic solution is optimal overall. The results have a number of consequences. For the Euclidean version of the problem, for instance, combining our results with known results on Euclidean TSP, yields a PTAS for approximating an optimal cyclic solution, and it yields a $(2(1-1/k)+\varepsilon)$-approximation of the optimal unrestricted solution. If the conjecture mentioned above is true, then our algorithm is actually a PTAS for the general problem in the Euclidean setting.

cs.CG↗

arXiv2022

Continual and Sliding Window Release for Private Empirical Risk Minimization

It is difficult to continually update private machine learning models with new data while maintaining privacy. Data incur increasing privacy loss -- as measured by differential privacy -- when they are used in repeated computations. In this paper, we describe regularized empirical risk minimization algorithms that continually release models for a recent window of data. One version of the algorithm uses the entire data history to improve the model for the recent window. The second version uses a sliding window of constant size to improve the model, ensuring more relevant models in case of evolving data. The algorithms operate in the framework of stochastic gradient descent. We prove that even with releasing a model at each time-step over an infinite time horizon, the privacy cost of any data point is bounded by a constant $ε$ differential privacy, and the accuracy of the output models are close to optimal. Experiments on MNIST and Arxiv publications data show results consistent with the theory.

cs.LG↗

arXiv2021

The Shapley Value of Classifiers in Ensemble Games

What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles, pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define \textit{Troupe} -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of models in these games is an effective decision metric for choosing a high performing subset of models from the ensemble. Our analytical findings prove that our Shapley value estimation scheme is precise and scalable; its performance increases with size of the dataset and ensemble. Empirical results on real world graph classification tasks demonstrate that our algorithm produces high quality estimates of the Shapley value. We find that Shapley values can be utilized for ensemble pruning, and that adversarial models receive a low valuation. Complex classifiers are frequently found to be responsible for both correct and incorrect classification decisions.

cs.LG↗

arXiv2021

PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models

We present PyTorch Geometric Temporal a deep learning framework combining state-of-the-art machine learning algorithms for neural spatiotemporal signal processing. The main goal of the library is to make temporal geometric deep learning available for researchers and machine learning practitioners in a unified easy-to-use framework. PyTorch Geometric Temporal was created with foundations on existing libraries in the PyTorch eco-system, streamlined neural network layer definitions, temporal snapshot generators for batching, and integrated benchmark datasets. These features are illustrated with a tutorial-like case study. Experiments demonstrate the predictive performance of the models implemented in the library on real world problems such as epidemiological forecasting, ridehail demand prediction and web-traffic management. Our sensitivity analysis of runtime shows that the framework can potentially operate on web-scale datasets with rich temporal features and spatial structure.

cs.LG↗

arXiv2021

Heterogeneous Interventions Reduce the Spread of COVID-19 in Simulations on Real Mobility Data

Major interventions have been introduced worldwide to slow down the spread of the SARS-CoV-2 virus. Large-scale lockdowns of human movements are effective in reducing the spread, but they come at a cost of significantly limited societal functions. We show that natural human movements are statistically diverse, and the spread of the disease is significantly influenced by a small group of active individuals and gathering venues. We find that interventions focused on these most mobile individuals and popular venues reduce both the peak infection rate and the total infected population while retaining high social activity levels. These trends are seen consistently in simulations with real human mobility data of different scales, resolutions, and modalities from multiple cities across the world. The observation implies that compared to broad sweeping interventions, more heterogeneous strategies that are targeted based on the network effects in human mobility provide a better balance between pandemic control and regular social activities.

cs.SI↗

arXiv2021

Multi-scale Attributed Node Embedding

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

cs.LG↗

arXiv2021

Twitch Gamers: a Dataset for Evaluating Proximity Preserving and Structural Role-based Node Embeddings

Proximity preserving and structural role-based node embeddings have become a prime workhorse of applied graph mining. Novel node embedding techniques are often tested on a restricted set of benchmark datasets. In this paper, we propose a new diverse social network dataset called Twitch Gamers with multiple potential target attributes. Our analysis of the social network and node classification experiments illustrate that Twitch Gamers is suitable for assessing the predictive performance of novel proximity preserving and structural role-based node embedding algorithms.

cs.SI↗

arXiv2021

Chickenpox Cases in Hungary: a Benchmark Dataset for Spatiotemporal Signal Processing with Graph Neural Networks

Recurrent graph convolutional neural networks are highly effective machine learning techniques for spatiotemporal signal processing. Newly proposed graph neural network architectures are repetitively evaluated on standard tasks such as traffic or weather forecasting. In this paper, we propose the Chickenpox Cases in Hungary dataset as a new dataset for comparing graph neural network architectures. Our time series analysis and forecasting experiments demonstrate that the Chickenpox Cases in Hungary dataset is adequate for comparing the predictive performance and forecasting capabilities of novel recurrent graph neural network architectures.

cs.LG↗

arXiv2021

Euler Characteristic Surfaces

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of random fields. The goal of this paper is to present the extension of using the Euler characteristic in higher-dimensional parameter spaces. While topological data analysis of higher-dimensional parameter spaces using stronger invariants such as homology continues to be the subject of intense research, Euler characteristic is more manageable theoretically and computationally, and this analysis can be seen as an important intermediary step in multi-parameter topological data analysis. We show the usefulness of the techniques using artificially generated examples, and a real-world application of detecting diabetic retinopathy in retinal images.

math.AT↗

arXiv2020

Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models

In this paper, we propose a flexible notion of characteristic functions defined on graph vertices to describe the distribution of vertex features at multiple scales. We introduce FEATHER, a computationally efficient algorithm to calculate a specific variant of these characteristic functions where the probability weights of the characteristic function are defined as the transition probabilities of random walks. We argue that features extracted by this procedure are useful for node level machine learning tasks. We discuss the pooling of these node representations, resulting in compact descriptors of graphs that can serve as features for graph classification algorithms. We analytically prove that FEATHER describes isomorphic graphs with the same representation and exhibits robustness to data corruption. Using the node feature characteristic functions we define parametric models where evaluation points of the functions are learned parameters of supervised classifiers. Experiments on real world large datasets show that our proposed algorithm creates high quality representations, performs transfer learning efficiently, exhibits robustness to hyperparameter changes, and scales linearly with the input size.

cs.LG↗

arXiv2020

Little Ball of Fur: A Python Library for Graph Sampling

Sampling graphs is an important task in data mining. In this paper, we describe Little Ball of Fur a Python library that includes more than twenty graph sampling algorithms. Our goal is to make node, edge, and exploration-based network sampling techniques accessible to a large number of professionals, researchers, and students in a single streamlined framework. We created this framework with a focus on a coherent application public interface which has a convenient design, generic input data requirements, and reasonable baseline settings of algorithms. Here we overview these design foundations of the framework in detail with illustrative code snippets. We show the practical usability of the library by estimating various global statistics of social networks and web graphs. Experiments demonstrate that Little Ball of Fur can speed up node and whole graph embedding techniques considerably with mildly deteriorating the predictive value of distilled features.

cs.SI↗

arXiv2020

Karate Club: An API Oriented Open-source Python Framework for Unsupervised Learning on Graphs

We present Karate Club a Python framework combining more than 30 state-of-the-art graph mining algorithms which can solve unsupervised machine learning tasks. The primary goal of the package is to make community detection, node and whole graph embedding available to a wide audience of machine learning researchers and practitioners. We designed Karate Club with an emphasis on a consistent application interface, scalability, ease of use, sensible out of the box model behaviour, standardized dataset ingestion, and output generation. This paper discusses the design principles behind this framework with practical examples. We show Karate Club's efficiency with respect to learning performance on a wide range of real world clustering problems, classification tasks and support evidence with regards to its competitive speed.

cs.LG↗

arXiv2020

Approximation Algorithms for Multi-Robot Patrol-Scheduling with Min-Max Latency

We consider the problem of finding patrol schedules for $k$ robots to visit a given set of $n$ sites in a metric space. Each robot has the same maximum speed and the goal is to minimize the weighted maximum latency of any site, where the latency of a site is defined as the maximum time duration between consecutive visits of that site. The problem is NP-hard, as it has the traveling salesman problem as a special case (when $k=1$ and all sites have the same weight). We present a polynomial-time algorithm with an approximation factor of $O(k^2 \log \frac{w_{\max}}{w_{\min}})$ to the optimal solution, where $w_{\max}$ and $w_{\min}$ are the maximum and minimum weight of the sites respectively. Further, we consider the special case where the sites are in 1D. When all sites have the same weight, we present a polynomial-time algorithm to solve the problem exactly. If the sites may have different weights, we present a $12$-approximate solution, which runs in polynomial time when the number of robots, $k$, is a constant.

cs.DS↗

arXiv2020

Stability Enhanced Privacy and Applications in Private Stochastic Gradient Descent

Private machine learning involves addition of noise while training, resulting in lower accuracy. Intuitively, greater stability can imply greater privacy and improve this privacy-utility tradeoff. We study this role of stability in private empirical risk minimization, where differential privacy is achieved by output perturbation, and establish a corresponding theoretical result showing that for strongly-convex loss functions, an algorithm with uniform stability of $β$ implies a bound of $O(\sqrtβ)$ on the scale of noise required for differential privacy. The result applies to both explicit regularization and to implicitly stabilized ERM, such as adaptations of Stochastic Gradient Descent that are known to be stable. Thus, it generalizes recent results that improve privacy through modifications to SGD, and establishes stability as the unifying perspective. It implies new privacy guarantees for optimizations with uniform stability guarantees, where a corresponding differential privacy guarantee was previously not known. Experimental results validate the utility of stability enhanced privacy in several problems, including application of elastic nets and feature selection.

cs.LG↗

arXiv2020

Fast Sequence-Based Embedding with Diffusion Graphs

A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear sequences of nodes to create embeddings using a neural network. In this paper, we propose diffusion graphs as a method to rapidly generate vertex sequences for network embedding. Its computational efficiency is superior to previous methods due to simpler sequence generation, and it produces more accurate results. In experiments, we found that the performance relative to other methods improves with increasing edge density in the graph. In a community detection task, clustering nodes in the embedding space produces better results compared to other sequence-based embedding methods.

cs.LG↗

arXiv2019

GEMSEC: Graph Embedding with Self Clustering

Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding. GEMSEC is a general extension of earlier work in the domain of sequence-based graph embedding. GEMSEC places nodes in an abstract feature space where the vertex features minimize the negative log-likelihood of preserving sampled vertex neighborhoods, and it incorporates known social network properties through a machine learning regularization. We present two new social network datasets and show that by simultaneously considering the embedding and clustering problems with respect to social properties, GEMSEC extracts high-quality clusters competitive with or superior to other community detection algorithms. In experiments, the method is found to be computationally efficient and robust to the choice of hyperparameters.

cs.SI↗

arXiv2016

Distributed Submodular Maximization

Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular set function subject to various constraints. Classical approaches to submodular optimization require centralized access to the full dataset, which is impractical for truly large-scale problems. In this paper, we consider the problem of submodular function maximization in a distributed fashion. We develop a simple, two-stage protocol GreeDi, that is easily implemented using MapReduce style computations. We theoretically analyze our approach, and show that under certain natural conditions, performance close to the centralized approach can be achieved. We begin with monotone submodular maximization subject to a cardinality constraint, and then extend this approach to obtain approximation guarantees for (not necessarily monotone) submodular maximization subject to more general constraints including matroid or knapsack constraints. In our extensive experiments, we demonstrate the effectiveness of our approach on several applications, including sparse Gaussian process inference and exemplar based clustering on tens of millions of examples using Hadoop.

cs.LG↗