arXiv subjects

Arindam Banerjee

Publications and source records attributed to Arindam Banerjee.

At least 73 records · Page 4Linked to original sources

arXiv2019

Hessian based analysis of SGD for Deep Nets: Dynamics and Generalization

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new empirical observations and theoretical results on both the optimization dynamics and generalization behavior of SGD for deep nets based on the Hessian of the training loss and associated quantities. We consider three specific research questions: (1) what is the relationship between the Hessian of the loss and the second moment of stochastic gradients (SGs)? (2) how can we characterize the stochastic optimization dynamics of SGD with fixed and adaptive step sizes and diagonal pre-conditioning based on the first and second moments of SGs? and (3) how can we characterize a scale-invariant generalization bound of deep nets based on the Hessian of the loss, which by itself is not scale invariant? We shed light on these three questions using theoretical results supported by extensive empirical observations, with experiments on synthetic data, MNIST, and CIFAR-10, with different batch sizes, and with different difficulty levels by synthetically adding random labels.

cs.LG↗

arXiv2019

Performance and near-wake characterization of a tidal current turbine in elevated levels of free stream turbulence

Tidal turbines are deployed in sites which have elevated levels of free stream turbulence (FST). Accounting for elevated FST on their operation become vital from a design standpoint. Detailed experimental measurements of the dynamic near-wake of a tidal turbine model in elevated FST environments is presented; an active grid turbulence generator developed by our group was used to seed in the elevated FST and evaluate the influence of turbulence intensity (Ti) and inflow integral length scale (L) on the near-wake of the turbine. Three inflow conditions are tested: a quasi-laminar flow with Ti ~ 2.2% and two elevated Ti (~12-14%) cases, one with L ~ 0.4D (D is the turbine diameter) and the other where L~ D. Elevated Ti cases was found to increase the standard deviation of rotor torque by 4.5 times the value in quasi-laminar flow. Energy recovery was also found to be accelerated; at X/D=4, the percentage of inflow energy recovered was 37% and was twice the corresponding value in quasi-laminar flow. Elevated FST was observed to disrupt the rotational character of the wake; the drop in swirl number ranged between 12% at X/D=0.5 to 71% at X/D=4. Elevated Ti also resulted in L that were considerably larger (> 2 times) than the quasi-laminar flow case. An increase in inflow integral length scale (from 0.4D to D) was observed to result in enhanced wake Ti, wake structures and anisotropy; however, no noticeable influence was found on the rate of wake recovery.

physics.flu-dyn↗

arXiv2019

Two-block vs. Multi-block ADMM: An empirical evaluation of convergence

Alternating Direction Method of Multipliers (ADMM) has become a widely used optimization method for convex problems, particularly in the context of data mining in which large optimization problems are often encountered. ADMM has several desirable properties, including the ability to decompose large problems into smaller tractable sub-problems and ease of parallelization, that are essential in these scenarios. The most common form of ADMM is the two-block, in which two sets of primal variables are updated alternatingly. Recent years have seen advances in multi-block ADMM, which update more than two blocks of primal variables sequentially. In this paper, we study the empirical question: {\em Is two-block ADMM always comparable with sequential multi-block ADMM solving an equivalent problem?} In the context of optimization problems arising in multi-task learning, through a comprehensive set of experiments we surprisingly show that multi-block ADMM consistently outperformed two-block ADMM on optimization performance, and as a consequence on prediction performance, across all datasets and for the entire range of dual step sizes. Our results have an important practical implication: rather than simply using the popular two-block ADMM, one may considerably benefit from experimenting with multi-block ADMM applied to an equivalent problem.

stat.ML↗

arXiv2019

Regularity of powers of edge ideals: from local properties to global bounds

Let $I = I(G)$ be the edge ideal of a graph $G$. We give various general upper bounds for the regularity function $\text{reg} I^s$, for $s \ge 1$, addressing a conjecture made by the authors and Alilooee. When $G$ is a gap-free graph and locally of regularity 2, we show that $\text{reg} I^s = 2s$ for all $s \ge 2$. This is a slightly weaker version of a conjecture of Nevo and Peeva. Our method is to investigate the regularity function $\text{reg}I^s$, for $s \ge 1$, via local information of $I$.

math.AC↗

arXiv2018

Unified View of Matrix Completion under General Structural Constraints

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix completion, and provide unified upper bounds on the sample complexity and the estimation error. Our analysis relies on results from generic chaining, and we establish two intermediate results of independent interest: (a) in characterizing the size or complexity of low dimensional subsets in high dimensional ambient space, a certain partial complexity measure encountered in the analysis of matrix completion problems is characterized in terms of a well understood complexity measure of Gaussian widths, and (b) it is shown that a form of restricted strong convexity holds for matrix completion problems under general norm regularization. Further, we provide several non-trivial examples of structures included in our framework, notably the recently proposed spectral $k$-support norm.

stat.ML↗

arXiv2018

DAPPER: Scaling Dynamic Author Persona Topic Model to Billion Word Corpora

Extracting common narratives from multi-author dynamic text corpora requires complex models, such as the Dynamic Author Persona (DAP) topic model. However, such models are complex and can struggle to scale to large corpora, often because of challenging non-conjugate terms. To overcome such challenges, in this paper we adapt new ideas in approximate inference to the DAP model, resulting in the DAP Performed Exceedingly Rapidly (DAPPER) topic model. Specifically, we develop Conjugate-Computation Variational Inference (CVI) based variational Expectation-Maximization (EM) for learning the model, yielding fast, closed form updates for each document, replacing iterative optimization in earlier work. Our results show significant improvements in model fit and training time without needing to compromise the model's temporal structure or the application of Regularized Variation Inference (RVI). We demonstrate the scalability and effectiveness of the DAPPER model by extracting health journeys from the CaringBridge corpus --- a collection of 9 million journals written by 200,000 authors during health crises.

stat.ML↗

arXiv2018

Adversarial Recommendation: Attack of the Learned Fake Users

Can machine learning models for recommendation be easily fooled? While the question has been answered for hand-engineered fake user profiles, it has not been explored for machine learned adversarial attacks. This paper attempts to close this gap. We propose a framework for generating fake user profiles which, when incorporated in the training of a recommendation system, can achieve an adversarial intent, while remaining indistinguishable from real user profiles. We formulate this procedure as a repeated general-sum game between two players: an oblivious recommendation system $R$ and an adversarial fake user generator $A$ with two goals: (G1) the rating distribution of the fake users needs to be close to the real users, and (G2) some objective $f_A$ encoding the attack intent, such as targeting the top-K recommendation quality of $R$ for a subset of users, needs to be optimized. We propose a learning framework to achieve both goals, and offer extensive experiments considering multiple types of attacks highlighting the vulnerability of recommendation systems.

cs.IR↗

arXiv2018

Time Series Deinterleaving of DNS Traffic

Stream deinterleaving is an important problem with various applications in the cybersecurity domain. In this paper, we consider the specific problem of deinterleaving DNS data streams using machine-learning techniques, with the objective of automating the extraction of malware domain sequences. We first develop a generative model for user request generation and DNS stream interleaving. Based on these we evaluate various inference strategies for deinterleaving including augmented HMMs and LSTMs on synthetic datasets. Our results demonstrate that state-of-the-art LSTMs outperform more traditional augmented HMMs in this application domain.

cs.LG↗

arXiv2018

Revisiting Non-Progressive Influence Models: Scalable Influence Maximization

While influence maximization in social networks has been studied extensively in computer science community for the last decade the focus has been on the progressive influence models, such as independent cascade (IC) and Linear threshold (LT) models, which cannot capture the reversibility of choices. In this paper, we present the Heat Conduction (HC) model which is a non-progressive influence model with real-world interpretations. We show that HC unifies, generalizes, and extends the existing nonprogressive models, such as the Voter model [1] and non-progressive LT [2]. We then prove that selecting the optimal seed set of influential nodes is NP-hard for HC but by establishing the submodularity of influence spread, we can tackle the influence maximization problem with a scalable and provably near-optimal greedy algorithm. We are the first to present a scalable solution for influence maximization under nonprogressive LT model, as a special case of the HC model. In sharp contrast to the other greedy influence maximization methods, our fast and efficient C2GREEDY algorithm benefits from two analytically computable steps: closed-form computation for finding the influence spread as well as the greedy seed selection. Through extensive experiments on several large real and synthetic networks, we show that C2GREEDY outperforms the state-of-the-art methods, in terms of both influence spread and scalability.

cs.SI↗

arXiv2018

Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{reg} I(G)$ and the asymptotic linear function $\text{reg} I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$

math.AC↗

arXiv2018

Topic Modeling on Health Journals with Regularized Variational Inference

Topic modeling enables exploration and compact representation of a corpus. The CaringBridge (CB) dataset is a massive collection of journals written by patients and caregivers during a health crisis. Topic modeling on the CB dataset, however, is challenging due to the asynchronous nature of multiple authors writing about their health journeys. To overcome this challenge we introduce the Dynamic Author-Persona topic model (DAP), a probabilistic graphical model designed for temporal corpora with multiple authors. The novelty of the DAP model lies in its representation of authors by a persona --- where personas capture the propensity to write about certain topics over time. Further, we present a regularized variational inference algorithm, which we use to encourage the DAP model's personas to be distinct. Our results show significant improvements over competing topic models --- particularly after regularization, and highlight the DAP model's unique ability to capture common journeys shared by different authors.

cs.CL↗

arXiv2017

Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data

Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of data science models in enabling scientific discovery. The overarching vision of TGDS is to introduce scientific consistency as an essential component for learning generalizable models. Further, by producing scientifically interpretable models, TGDS aims to advance our scientific understanding by discovering novel domain insights. Indeed, the paradigm of TGDS has started to gain prominence in a number of scientific disciplines such as turbulence modeling, material discovery, quantum chemistry, bio-medical science, bio-marker discovery, climate science, and hydrology. In this paper, we formally conceptualize the paradigm of TGDS and present a taxonomy of research themes in TGDS. We describe several approaches for integrating domain knowledge in different research themes using illustrative examples from different disciplines. We also highlight some of the promising avenues of novel research for realizing the full potential of theory-guided data science.

cs.LG↗

arXiv2017

Sparse Linear Isotonic Models

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predictors; in particular, additive isotonic models (AIMs) assume the unknown transformations to be monotone. In this paper, we introduce sparse linear isotonic models (SLIMs) for highdimensional problems by hybridizing ideas in parametric sparse linear models and AIMs, which enjoy a few appealing advantages over both. In the high-dimensional setting, a two-step algorithm is proposed for estimating the sparse parameters as well as the monotone functions over predictors. Under mild statistical assumptions, we show that the algorithm can accurately estimate the parameters. Promising preliminary experiments are presented to support the theoretical results.

stat.ML↗

arXiv2017

High-Dimensional Dependency Structure Learning for Physical Processes

In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs (partial differential equations) and are observed in a variety of natural phenomena, including geoscience data capturing atmospheric and hydrological phenomena. Classical structure learning approaches such as the PC algorithm and variants are challenging to apply due to their high computational and sample requirements. Modern approaches, often based on sparse regression and variants, do come with finite sample guarantees, but are usually highly sensitive to the choice of hyper-parameters, e.g., parameter $λ$ for sparsity inducing constraint or regularization. In this paper, we present ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning, which estimates an edge specific parameter $λ_{ij}$ in the first step, and uses these parameters to learn the structure in the second step. Both steps of our algorithm use (inexact) ADMM to solve suitable linear programs, and all iterations can be done in closed form in an efficient block parallel manner. We compare ACLIME-ADMM with baselines on both synthetic data simulated by partial differential equations (PDEs) that model advection-diffusion processes, and real data (50 years) of daily global geopotential heights to study information flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and competitive, usually better than the baselines especially on difficult problems. On real data, ACLIME-ADMM recovers the underlying structure of global atmospheric circulation, including switches in wind directions at the equator and tropics entirely from the data.

cs.LG↗

arXiv2017

R2N2: Residual Recurrent Neural Networks for Multivariate Time Series Forecasting

Multivariate time-series modeling and forecasting is an important problem with numerous applications. Traditional approaches such as VAR (vector auto-regressive) models and more recent approaches such as RNNs (recurrent neural networks) are indispensable tools in modeling time-series data. In many multivariate time series modeling problems, there is usually a significant linear dependency component, for which VARs are suitable, and a nonlinear component, for which RNNs are suitable. Modeling such times series with only VAR or only RNNs can lead to poor predictive performance or complex models with large training times. In this work, we propose a hybrid model called R2N2 (Residual RNN), which first models the time series with a simple linear model (like VAR) and then models its residual errors using RNNs. R2N2s can be trained using existing algorithms for VARs and RNNs. Through an extensive empirical evaluation on two real world datasets (aviation and climate domains), we show that R2N2 is competitive, usually better than VAR or RNN, used alone. We also show that R2N2 is faster to train as compared to an RNN, while requiring less number of hidden units.

cs.LG↗

arXiv2017

High Dimensional Structured Superposition Models

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models which allow sum of any number of component parameters, and each component structure can be characterized by any norm. We present a simple estimator for such models, give a geometric condition under which the components can be accurately estimated, characterize sample complexity of the estimator, and give high probability non-asymptotic bounds on the componentwise estimation error. We use tools from empirical processes and generic chaining for the statistical analysis, and our results, which substantially generalize prior work on superposition models, are in terms of Gaussian widths of suitable sets.

cs.LG↗

arXiv2017

Recommendation under Capacity Constraints

In this paper, we investigate the common scenario where every candidate item for recommendation is characterized by a maximum capacity, i.e., number of seats in a Point-of-Interest (POI) or size of an item's inventory. Despite the prevalence of the task of recommending items under capacity constraints in a variety of settings, to the best of our knowledge, none of the known recommender methods is designed to respect capacity constraints. To close this gap, we extend three state-of-the art latent factor recommendation approaches: probabilistic matrix factorization (PMF), geographical matrix factorization (GeoMF), and bayesian personalized ranking (BPR), to optimize for both recommendation accuracy and expected item usage that respects the capacity constraints. We introduce the useful concepts of user propensity to listen and item capacity. Our experimental results in real-world datasets, both for the domain of item recommendation and POI recommendation, highlight the benefit of our method for the setting of recommendation under capacity constraints.

stat.ML↗

arXiv2017

Spatial Projection of Multiple Climate Variables using Hierarchical Multitask Learning

Future projection of climate is typically obtained by combining outputs from multiple Earth System Models (ESMs) for several climate variables such as temperature and precipitation. While IPCC has traditionally used a simple model output average, recent work has illustrated potential advantages of using a multitask learning (MTL) framework for projections of individual climate variables. In this paper we introduce a framework for hierarchical multitask learning (HMTL) with two levels of tasks such that each super-task, i.e., task at the top level, is itself a multitask learning problem over sub-tasks. For climate projections, each super-task focuses on projections of specific climate variables spatially using an MTL formulation. For the proposed HMTL approach, a group lasso regularization is added to couple parameters across the super-tasks, which in the climate context helps exploit relationships among the behavior of different climate variables at a given spatial location. We show that some recent works on MTL based on learning task dependency structures can be viewed as special cases of HMTL. Experiments on synthetic and real climate data show that HMTL produces better results than decoupled MTL methods applied separately on the super-tasks and HMTL significantly outperforms baselines for climate projection.

cs.LG↗