arXiv subjects

Haris Vikalo

Publications and source records attributed to Haris Vikalo.

At least 55 records · Page 3Linked to original sources

arXiv2020

Communication-Efficient Federated Learning via Optimal Client Sampling

Federated learning (FL) ameliorates privacy concerns in settings where a central server coordinates learning from data distributed across many clients. The clients train locally and communicate the models they learn to the server; aggregation of local models requires frequent communication of large amounts of information between the clients and the central server. We propose a novel, simple and efficient way of updating the central model in communication-constrained settings based on collecting models from clients with informative updates and estimating local updates that were not communicated. In particular, modeling the progression of model's weights by an Ornstein-Uhlenbeck process allows us to derive an optimal sampling strategy for selecting a subset of clients with significant weight updates. The central server collects updated local models from only the selected clients and combines them with estimated model updates of the clients that were not selected for communication. We test this policy on a synthetic dataset for logistic regression and two FL benchmarks, namely, a classification task on EMNIST and a realistic language modeling task using the Shakespeare dataset. The results demonstrate that the proposed framework provides significant reduction in communication while maintaining competitive or achieving superior performance compared to a baseline. Our method represents a new line of strategies for communication-efficient FL that is orthogonal to the existing user-local methods such as quantization or sparsification, thus complementing rather than aiming to replace those existing methods.

cs.LG↗

arXiv2020

A Study of the Learnability of Relational Properties: Model Counting Meets Machine Learning (MCML)

This paper introduces the MCML approach for empirically studying the learnability of relational properties that can be expressed in the well-known software design language Alloy. A key novelty of MCML is quantification of the performance of and semantic differences among trained machine learning (ML) models, specifically decision trees, with respect to entire (bounded) input spaces, and not just for given training and test datasets (as is the common practice). MCML reduces the quantification problems to the classic complexity theory problem of model counting, and employs state-of-the-art model counters. The results show that relatively simple ML models can achieve surprisingly high performance (accuracy and F1-score) when evaluated in the common setting of using training and test datasets - even when the training dataset is much smaller than the test dataset - indicating the seeming simplicity of learning relational properties. However, MCML metrics based on model counting show that the performance can degrade substantially when tested against the entire (bounded) input space, indicating the high complexity of precisely learning these properties, and the usefulness of model counting in quantifying the true performance.

cs.LG↗

arXiv2020

Identifying Sparse Low-Dimensional Structures in Markov Chains: A Nonnegative Matrix Factorization Approach

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the kernel space. The kernel space contains a set of meta states which are desired to be representative of only a small subset of original states. To promote this structural property, we constrain the number of nonzero entries of the mappings between the state space and the kernel space. By imposing the desired characteristics of the representation, we cast the problem as a constrained nonnegative matrix factorization. To compute the solution, we propose an efficient block coordinate gradient descent and theoretically analyze its convergence properties.

cs.LG↗

arXiv2020

Federating Recommendations Using Differentially Private Prototypes

Machine learning methods allow us to make recommendations to users in applications across fields including entertainment, dating, and commerce, by exploiting similarities in users' interaction patterns. However, in domains that demand protection of personally sensitive data, such as medicine or banking, how can we learn such a model without accessing the sensitive data, and without inadvertently leaking private information? We propose a new federated approach to learning global and local private models for recommendation without collecting raw data, user statistics, or information about personal preferences. Our method produces a set of prototypes that allows us to infer global behavioral patterns, while providing differential privacy guarantees for users in any database of the system. By requiring only two rounds of communication, we both reduce the communication costs and avoid the excessive privacy loss associated with iterative procedures. We test our framework on synthetic data as well as real federated medical data and Movielens ratings data. We show local adaptation of the global model allows our method to outperform centralized matrix-factorization-based recommender system models, both in terms of accuracy of matrix reconstruction and in terms of relevance of the recommendations, while maintaining provable privacy guarantees. We also show that our method is more robust and is characterized by smaller variance than individual models learned by independent entities.

cs.IR↗

arXiv2019

Evolutionary Clustering via Message Passing

We are often interested in clustering objects that evolve over time and identifying solutions to the clustering problem for every time step. Evolutionary clustering provides insight into cluster evolution and temporal changes in cluster memberships while enabling performance superior to that achieved by independently clustering data collected at different time points. In this paper we introduce evolutionary affinity propagation (EAP), an evolutionary clustering algorithm that groups data points by exchanging messages on a factor graph. EAP promotes temporal smoothness of the solution to clustering time-evolving data by linking the nodes of the factor graph that are associated with adjacent data snapshots, and introduces consensus nodes to enable cluster tracking and identification of cluster births and deaths. Unlike existing evolutionary clustering methods that require additional processing to approximate the number of clusters or match them across time, EAP determines the number of clusters and tracks them automatically. A comparison with existing methods on simulated and experimental data demonstrates effectiveness of the proposed EAP algorithm.

cs.LG↗

arXiv2019

ComHapDet: A Spatial Community Detection Algorithm for Haplotype Assembly

Background: Haplotypes, the ordered lists of single nucleotide variations that distinguish chromosomal sequences from their homologous pairs, may reveal an individual's susceptibility to hereditary and complex diseases and affect how our bodies respond to therapeutic drugs. Reconstructing haplotypes of an individual from short sequencing reads is an NP-hard problem that becomes even more challenging in the case of polyploids. While increasing lengths of sequencing reads and insert sizes {\color{black} helps improve accuracy of reconstruction}, it also exacerbates computational complexity of the haplotype assembly task. This has motivated the pursuit of algorithmic frameworks capable of accurate yet efficient assembly of haplotypes from high-throughput sequencing data. Results: We propose a novel graphical representation of sequencing reads and pose the haplotype assembly problem as an instance of community detection on a spatial random graph. To this end, we construct a graph where each read is a node with an unknown community label associating the read with the haplotype it samples. Haplotype reconstruction can then be thought of as a two-step procedure: first, one recovers the community labels on the nodes (i.e., the reads), and then uses the estimated labels to assemble the haplotypes. Based on this observation, we propose ComHapDet - a novel assembly algorithm for diploid and ployploid haplotypes which allows both bialleleic and multi-allelic variants. Conclusions: Performance of the proposed algorithm is benchmarked on simulated as well as experimental data obtained by sequencing Chromosome $5$ of tetraploid biallelic \emph{Solanum-Tuberosum} (Potato). The results demonstrate the efficacy of the proposed method and that it compares favorably with the existing techniques.

cs.SI↗

arXiv2019

A Graph Auto-Encoder for Haplotype Assembly and Viral Quasispecies Reconstruction

Reconstructing components of a genomic mixture from data obtained by means of DNA sequencing is a challenging problem encountered in a variety of applications including single individual haplotyping and studies of viral communities. High-throughput DNA sequencing platforms oversample mixture components to provide massive amounts of reads whose relative positions can be determined by mapping the reads to a known reference genome; assembly of the components, however, requires discovery of the reads' origin -- an NP-hard problem that the existing methods struggle to solve with the required level of accuracy. In this paper, we present a learning framework based on a graph auto-encoder designed to exploit structural properties of sequencing data. The algorithm is a neural network which essentially trains to ignore sequencing errors and infers the posteriori probabilities of the origin of sequencing reads. Mixture components are then reconstructed by finding consensus of the reads determined to originate from the same genomic component. Results on realistic synthetic as well as experimental data demonstrate that the proposed framework reliably assembles haplotypes and reconstructs viral communities, often significantly outperforming state-of-the-art techniques.

q-bio.GN↗

arXiv2019

Submodular Observation Selection and Information Gathering for Quadratic Models

We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including feature selection, phase retrieval, and target localization. Since for quadratic measurement models the moment matrix of the optimal estimator is generally unknown, majority of prior work resorts to approximation techniques such as linearization of the observation model to optimize the alphabetical optimality criteria of an approximate moment matrix. Conversely, by exploiting a connection to the classical Van Trees' inequality, we derive new alphabetical optimality criteria without distorting the relational structure of the observation model. We further show that under certain conditions on parameters of the problem these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for quadratic models, and provide theoretical bounds on its achievable utility.

eess.SP↗

arXiv2018

Evolutionary Self-Expressive Models for Subspace Clustering

The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points that lie on a union of low-dimensional evolving subspaces. To learn the parsimonious representation of the data points at each time step, we propose a non-convex optimization framework that exploits the self-expressiveness property of the evolving data while taking into account representation from the preceding time step. To find an approximate solution to the aforementioned non-convex optimization problem, we develop a scheme based on alternating minimization that both learns the parsimonious representation as well as adaptively tunes and infers a smoothing parameter reflective of the rate of data evolution. The latter addresses a fundamental challenge in evolutionary clustering -- determining if and to what extent one should consider previous clustering solutions when analyzing an evolving data collection. Our experiments on both synthetic and real-world datasets demonstrate that the proposed framework outperforms state-of-the-art static subspace clustering algorithms and existing evolutionary clustering schemes in terms of both accuracy and running time, in a range of scenarios.

cs.CV↗

arXiv2018

Blind nucleosynthetic source discovery in astronomical elemental abundance data

We demonstrate physics-blind and purely data-based nucleosynthetic archetype discovery from heterogeneous stellar elemental abundance measurements. Archetype extraction is performed via non-negative matrix factorization (NMF). Because stellar elemental abundance measurements can be incomplete and sparsely sampled, we perform combined low-rank NMF and matrix completion on the Hypatia Catalog and JINAbase to extract archetypal elemental abundance patterns, the so-called endmembers, and impute the missing measurements. We qualitatively compare the discovered nucleosynthetic archetypes to patterns anticipated from direct astrophysical nucleosynthetic calculations. Our tentative results indicate that the physics-blind analysis relying entirely on the incomplete chemical mixing in star formation can discern nucleosynthetic archetypes associated with asymptotic giant branch (AGB) stellar sources of the s-process, thermonuclear supernovae, and non-thermonuclear supernovae with an r-process.

astro-ph.SR↗

arXiv2018

Near-Optimal Distributed Estimation for a Network of Sensing Units Operating Under Communication Constraints

We study the problem of distributed state estimation in a network of sensing units that can exchange their measurements but the rate of communication between the units is constrained. The units collect noisy, possibly only partial observations of the unknown state; they are assisted by a relay center which can communicate at a higher rate and schedules the exchange of measurements between the units. We consider the task of minimizing the total mean-square estimation error of the network while promoting balance between the individual units' performances. This problem is formulated as the maximization of a monotone objective function subject to a cardinality constraint. By leveraging the notion of weak submodularity, we develop an efficient greedy algorithm for the proposed formulation and show that the greedy algorithm achieves a constant factor approximation of the optimal objective. Our extensive simulation studies illustrate the efficacy of the proposed formulation and the greedy algorithm.

eess.SP↗

arXiv2018

Randomized Greedy Sensor Selection: Leveraging Weak Submodularity

We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space model and the resource are unlimited, the conventional Kalman filter provides the minimum mean-square error (MMSE) estimates. However, at any given time, restrictions on the available communications bandwidth and computational capabilities and/or power impose a limitation on the number of network nodes whose observations can be used to compute the estimates. We formulate the problem of selecting the most informative subset of the sensors as a combinatorial problem of maximizing a monotone set function under a uniform matroid constraint. For the MMSE estimation criterion we show that the maximum element-wise curvature of the objective function satisfies a certain upper-bound constraint and is, therefore, weak submodular. We develop an efficient randomized greedy algorithm for sensor selection and establish guarantees on the estimator's performance in this setting. Extensive simulation results demonstrate the efficacy of the randomized greedy algorithm compared to state-of-the-art greedy and semidefinite programming relaxation methods.

eess.SP↗

arXiv2018

A Novel Scheme for Support Identification and Iterative Sampling of Bandlimited Graph Signals

We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction error. We propose an efficient iterative selection sampling approach and show that in the noiseless case the original signal is exactly recovered from the set of selected nodes. In the case of noisy measurements, a bound on the reconstruction error of the proposed algorithm is established. We further address the support identification of the bandlimited signal with unknown support and show that under a pragmatic sufficient condition, the proposed framework requires minimal number of samples to perfectly identify the support. The efficacy of the proposed methods are illustrated through numerical simulations on synthetic and real-world graphs.

eess.SP↗

arXiv2018

Matrix Completion and Performance Guarantees for Single Individual Haplotyping

Single individual haplotyping is an NP-hard problem that emerges when attempting to reconstruct an organism's inherited genetic variations using data typically generated by high-throughput DNA sequencing platforms. Genomes of diploid organisms, including humans, are organized into homologous pairs of chromosomes that differ from each other in a relatively small number of variant positions. Haplotypes are ordered sequences of the nucleotides in the variant positions of the chromosomes in a homologous pair; for diploids, haplotypes associated with a pair of chromosomes may be conveniently represented by means of complementary binary sequences. In this paper, we consider a binary matrix factorization formulation of the single individual haplotyping problem and efficiently solve it by means of alternating minimization. We analyze the convergence properties of the alternating minimization algorithm and establish theoretical bounds for the achievable haplotype reconstruction error. The proposed technique is shown to outperform existing methods when applied to synthetic as well as real-world Fosmid-based HapMap NA12878 datasets.

cs.LG↗

arXiv2018

Sampling Requirements and Accelerated Schemes for Sparse Linear Regression with Orthogonal Least-Squares

We study the problem of inferring a sparse vector from random linear combinations of its components. We propose the Accelerated Orthogonal Least-Squares (AOLS) algorithm that improves performance of the well-known Orthogonal Least-Squares (OLS) algorithm while requiring significantly lower computational costs. While OLS greedily selects columns of the coefficient matrix that correspond to non-zero components of the sparse vector, AOLS employs a novel computationally efficient procedure that speeds up the search by anticipating future selections via choosing $L$ columns in each step, where $L$ is an adjustable hyper-parameter. We analyze the performance of AOLS and establish lower bounds on the probability of exact recovery for both noiseless and noisy random linear measurements. In the noiseless scenario, it is shown that when the coefficients are samples from a Gaussian distribution, AOLS with high probability recovers a $k$-sparse $m$-dimensional sparse vector using ${\cal O}(k\log \frac{m}{k+L-1})$ measurements. Similar result is established for the bounded-noise scenario where an additional condition on the smallest nonzero element of the unknown vector is required. The asymptotic sampling complexity of AOLS is lower than the asymptotic sampling complexity of the existing sparse reconstruction algorithms. In simulations, AOLS is compared to state-of-the-art sparse recovery techniques and shown to provide better performance in terms of accuracy, running time, or both. Finally, we consider an application of AOLS to clustering high-dimensional data lying on the union of low-dimensional subspaces and demonstrate its superiority over existing methods.

stat.ML↗

arXiv2018

A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks

We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as the maximization of a monotone set function under a matroid constraint. We propose a randomized greedy algorithm that is significantly faster than state-of-the-art methods. By introducing the notion of curvature which quantifies how close a function is to being submodular, we analyze the performance of the proposed algorithm and find a bound on the expected mean square error (MSE) of the estimator that uses the selected sensors in terms of the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for the scenario where{\color{black}{ the measurements are i.i.d. random vectors with bounded $\ell_2$ norm.}} Simulation results demonstrate efficacy of the randomized greedy algorithm in a comparison with greedy and semidefinite programming relaxation methods.

eess.SY↗

arXiv2017

Accelerated Sparse Subspace Clustering

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practice while the performance of OMP-based schemes are unsatisfactory, especially in settings where data points are highly similar. In this paper, we propose a novel algorithm that exploits an accelerated variant of orthogonal least-squares to efficiently find the underlying subspaces. We show that under certain conditions the proposed algorithm returns a subspace-preserving solution. Simulation results illustrate that the proposed method compares favorably with BP-based method in terms of running time while being significantly more accurate than OMP-based schemes.

cs.LG↗

arXiv2017

Sampling and Reconstruction of Graph Signals via Weak Submodularity and Semidefinite Relaxation

We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end, we formulate the task at hand as the minimization of MSE subject to binary constraints, and approximate the resulting NP-hard problem via semidefinite programming (SDP) relaxation. Moreover, we provide an alternative formulation based on maximizing a monotone weak submodular function and propose a randomized-greedy algorithm to find a sub-optimal subset. We then derive a worst-case performance guarantee on the MSE returned by the randomized greedy algorithm for general non-stationary graph signals. The efficacy of the proposed methods is illustrated through numerical simulations on synthetic and real-world graphs. Notably, the randomized greedy algorithm yields an order-of-magnitude speedup over state-of-the-art greedy sampling schemes, while incurring only a marginal MSE performance loss.

stat.ML↗