arXiv subjects

Taposh Banerjee

Publications and source records attributed to Taposh Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2022

Where Should Traffic Sensors Be Placed on Highways?

This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis -- jointly with integer programming -- to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics.

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arXiv2020

Asymmetric Cell Transmission Model-Based, Ramp-Connected Robust Traffic Density Estimation under Bounded Disturbances

In modern transportation systems, traffic congestion is inevitable. To minimize the loss caused by congestion, various control strategies have been developed most of which rely on observing real-time traffic conditions. As vintage traffic sensors are limited, traffic density estimation is very helpful for gaining network-wide observability. This paper deals with this problem by first, presenting a traffic model for stretched highway having multiple ramps built based on asymmetric cell transmission model (ACTM). Second, based on the assumption that the encompassed nonlinearity of the ACTM is Lipschitz, a robust dynamic observer framework for performing traffic density estimation is proposed. Numerical test results show that the observer yields a sufficient performance in estimating traffic densities having noisy measurements, while being computationally faster the Unscented Kalman Filter in performing real-time estimation.

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arXiv2020

Cross-subject Decoding of Eye Movement Goals from Local Field Potentials

Objective. We consider the cross-subject decoding problem from local field potential (LFP) signals, where training data collected from the prefrontal cortex (PFC) of a source subject is used to decode intended motor actions in a destination subject. Approach. We propose a novel supervised transfer learning technique, referred to as data centering, which is used to adapt the feature space of the source to the feature space of the destination. The key ingredients of data centering are the transfer functions used to model the deterministic component of the relationship between the source and destination feature spaces. We propose an efficient data-driven estimation approach for linear transfer functions that uses the first and second order moments of the class-conditional distributions. Main result. We apply our data centering technique with linear transfer functions for cross-subject decoding of eye movement intentions in an experiment where two macaque monkeys perform memory-guided visual saccades to one of eight target locations. The results show peak cross-subject decoding performance of $80\%$, which marks a substantial improvement over random choice decoder. In addition to this, data centering also outperforms standard sampling-based methods in setups with imbalanced training data. Significance. The analyses presented herein demonstrate that the proposed data centering is a viable novel technique for reliable LFP-based cross-subject brain-computer interfacing and neural prostheses.

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arXiv2019

Minimax-Optimal Algorithms for Detecting Changes in Statistically Periodic Random Processes

Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new class of stochastic processes proposed by us. An algorithm is developed that is minimax asymptotically optimal as the false alarm rate goes to zero. Algorithms are also developed for the cases when the post-change distribution is not known or when there are multiple streams of observations. The modeling is inspired by real datasets encountered in cyber-physical systems, biology, and medicine. The developed algorithms are applied to sequences of Instagram counts collected around a 5K run in New York City to detect the run.

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arXiv2019

A Bayesian Theory of Change Detection in Statistically Periodic Random Processes

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. A novel Bayesian theory is developed for detecting a change in the distribution of an i.p.i.d. process. It is shown that the Bayesian change point problem can be expressed as a problem of optimal control of a Markov decision process (MDP) with periodic transition and cost structures. Optimal control theory is developed for periodic MDPs for discounted and undiscounted total cost criteria. A fixed-point equation is obtained that is satisfied by the optimal cost function. It is shown that the optimal policy for the MDP is nonstationary but periodic in nature. A value iteration algorithm is obtained to compute the optimal cost function. The results from the MDP theory are then applied to detect changes in i.p.i.d. processes. It is shown that while the optimal change point algorithm is a stopping rule based on a periodic sequence of thresholds, a single-threshold policy is asymptotically optimal, as the probability of false alarm goes to zero. Numerical results are provided to demonstrate that the asymptotically optimal policy is not strictly optimal.

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arXiv2019

Minimax-optimal decoding of movement goals from local field potentials using complex spectral features

We consider the problem of predicting eye movement goals from local field potentials (LFP) recorded through a multielectrode array in the macaque prefrontal cortex. The monkey is tasked with performing memory-guided saccades to one of eight targets during which LFP activity is recorded and used to train a decoder. Previous reports have mainly relied on the spectral amplitude of the LFPs as a feature in the decoding step to limited success, while neglecting the phase without proper theoretical justification. This paper formulates the problem of decoding eye movement intentions in a statistically optimal framework and uses Gaussian sequence modeling and Pinsker's theorem to generate minimax-optimal estimates of the LFP signals which are later used as features in the decoding step. The approach is shown to act as a low-pass filter and each LFP in the feature space is represented via its complex Fourier coefficients after appropriate shrinking such that higher frequency components are attenuated; this way, the phase information inherently present in the LFP signal is naturally embedded into the feature space. The proposed complex spectrum-based decoder achieves prediction accuracy of up to $94\%$ at superficial electrode depths near the surface of the prefrontal cortex, which marks a significant performance improvement over conventional power spectrum-based decoders.

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arXiv2018

Quickest Detection Of Deviations From Periodic Statistical Behavior

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d. processes. It is shown that the algorithms can be computed recursively and are asymptotically optimal. This problem has applications in anomaly detection in traffic data, social network data, and neural data, where periodic statistical behavior has been observed.

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arXiv2018

Sequential Detection of Regime Changes in Neural Data

The problem of detecting changes in firing patterns in neural data is studied. The problem is formulated as a quickest change detection problem. Important algorithms from the literature are reviewed. A new algorithmic technique is discussed to detect deviations from learned baseline behavior. The algorithms studied can be applied to both spike and local field potential data. The algorithms are applied to mice spike data to verify the presence of behavioral learning.

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arXiv2018

Cyclostationary Statistical Models and Algorithms for Anomaly Detection Using Multi-Modal Data

A framework is proposed to detect anomalies in multi-modal data. A deep neural network-based object detector is employed to extract counts of objects and sub-events from the data. A cyclostationary model is proposed to model regular patterns of behavior in the count sequences. The anomaly detection problem is formulated as a problem of detecting deviations from learned cyclostationary behavior. Sequential algorithms are proposed to detect anomalies using the proposed model. The proposed algorithms are shown to be asymptotically efficient in a well-defined sense. The developed algorithms are applied to a multi-modal data consisting of CCTV imagery and social media posts to detect a 5K run in New York City.

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arXiv2018

Quickest Detection for Changes in Maximal kNN Coherence of Random Matrices

This paper addresses the problem of quickest detection of a change in the maximal coherence between columns of a $n\times p$ random matrix based on a sequence of matrix observations having a single unknown change point. The random matrix is assumed to have identically distributed rows and the maximal coherence is defined as the largest of the $p \choose 2$ correlation coefficients associated with any row. Likewise, the $k$ nearest neighbor (kNN) coherence is defined as the $k$-th largest of these correlation coefficients. The forms of the pre- and post-change distributions of the observed matrices are assumed to belong to the family of elliptically contoured densities with sparse dispersion matrices but are otherwise unknown. A non-parametric stopping rule is proposed that is based on the maximal k-nearest neighbor sample coherence between columns of each observed random matrix. This is a summary statistic that is related to a test of the existence of a hub vertex in a sample correlation graph having a degree at least $k$. Performance bounds on the delay and false alarm performance of the proposed stopping rule are obtained in the purely high dimensional regime where $p\rightarrow \infty$ and $n$ is fixed. When the pre-change dispersion matrix is diagonal it is shown that, among all functions of the proposed summary statistic, the proposed stopping rule is asymptotically optimal under a minimax quickest change detection (QCD) model as the stopping threshold approaches infinity. The theory developed also applies to sequential hypothesis testing and fixed sample size tests.

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arXiv2018

Sequential Event Detection Using Multimodal Data in Nonstationary Environments

The problem of sequential detection of anomalies in multimodal data is considered. The objective is to observe physical sensor data from CCTV cameras, and social media data from Twitter and Instagram to detect anomalous behaviors or events. Data from each modality is transformed to discrete time count data by using an artificial neural network to obtain counts of objects in CCTV images and by counting the number of tweets or Instagram posts in a geographical area. The anomaly detection problem is then formulated as a problem of quickest detection of changes in count statistics. The quickest detection problem is then solved using the framework of partially observable Markov decision processes (POMDP), and structural results on the optimal policy are obtained. The resulting optimal policy is then applied to real multimodal data collected from New York City around a 5K race to detect the race. The count data both before and after the change is found to be nonstationary in nature. The proposed mathematical approach to this problem provides a framework for event detection in such nonstationary environments and across multiple data modalities.

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arXiv2017

Classification of Local Field Potentials using Gaussian Sequence Model

A problem of classification of local field potentials (LFPs), recorded from the prefrontal cortex of a macaque monkey, is considered. An adult macaque monkey is trained to perform a memory-based saccade. The objective is to decode the eye movement goals from the LFP collected during a memory period. The LFP classification problem is modeled as that of classification of smooth functions embedded in Gaussian noise. It is then argued that using minimax function estimators as features would lead to consistent LFP classifiers. The theory of Gaussian sequence models allows us to represent minimax estimators as finite dimensional objects. The LFP classifier resulting from this mathematical endeavor is a spectrum based technique, where Fourier series coefficients of the LFP data, followed by appropriate shrinkage and thresholding, are used as features in a linear discriminant classifier. The classifier is then applied to the LFP data to achieve high decoding accuracy. The function classification approach taken in the paper also provides a systematic justification for using Fourier series, with shrinkage and thresholding, as features for the problem, as opposed to using the power spectrum. It also suggests that phase information is crucial to the decision making.

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arXiv2017

Wavelet Shrinkage and Thresholding based Robust Classification for Brain Computer Interface

A macaque monkey is trained to perform two different kinds of tasks, memory aided and visually aided. In each task, the monkey saccades to eight possible target locations. A classifier is proposed for direction decoding and task decoding based on local field potentials (LFP) collected from the prefrontal cortex. The LFP time-series data is modeled in a nonparametric regression framework, as a function corrupted by Gaussian noise. It is shown that if the function belongs to Besov bodies, then using the proposed wavelet shrinkage and thresholding based classifier is robust and consistent. The classifier is then applied to the LFP data to achieve high decoding performance. The proposed classifier is also quite general and can be applied for the classification of other types of time-series data as well, not necessarily brain data.

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arXiv2017

Kiefer Wolfowitz Algorithm is Asymptotically Optimal for a Class of Non-Stationary Bandit Problems

We consider the problem of designing an allocation rule or an "online learning algorithm" for a class of bandit problems in which the set of control actions available at each time $s$ is a convex, compact subset of $\mathbb{R}^d$. Upon choosing an action $x$ at time $s$, the algorithm obtains a noisy value of the unknown and time-varying function $f_s$ evaluated at $x$. The "regret" of an algorithm is the gap between its expected reward, and the reward earned by a strategy which has the knowledge of the function $f_s$ at each time $s$ and hence chooses the action $x_s$ that maximizes $f_s$. For this non-stationary bandit problem set-up, we consider two variants of the Kiefer Wolfowitz (KW) algorithm i) KW with fixed step-size $β$, and ii) KW with sliding window of length $L$. We show that if the number of times that the function $f_s$ varies during time $T$ is $o(T)$, and if the learning rates of the proposed algorithms are chosen "optimally", then the regret of the proposed algorithms is $o(T)$, and hence the algorithms are asymptotically efficient.

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arXiv2017

Quickest Change Detection Approach to Optimal Control in Markov Decision Processes with Model Changes

Optimal control in non-stationary Markov decision processes (MDP) is a challenging problem. The aim in such a control problem is to maximize the long-term discounted reward when the transition dynamics or the reward function can change over time. When a prior knowledge of change statistics is available, the standard Bayesian approach to this problem is to reformulate it as a partially observable MDP (POMDP) and solve it using approximate POMDP solvers, which are typically computationally demanding. In this paper, the problem is analyzed through the viewpoint of quickest change detection (QCD), a set of tools for detecting a change in the distribution of a sequence of random variables. Current methods applying QCD to such problems only passively detect changes by following prescribed policies, without optimizing the choice of actions for long term performance. We demonstrate that ignoring the reward-detection trade-off can cause a significant loss in long term rewards, and propose a two threshold switching strategy to solve the issue. A non-Bayesian problem formulation is also proposed for scenarios where a Bayesian formulation cannot be defined. The performance of the proposed two threshold strategy is examined through numerical analysis on a non-stationary MDP task, and the strategy outperforms the state-of-the-art QCD methods in both Bayesian and non-Bayesian settings.

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arXiv2017

Quickest Hub Discovery in Correlation Graphs

A sequential test is proposed for detection and isolation of hubs in a correlation graph. Hubs in a correlation graph of a random vector are variables (nodes) that have a strong correlation edge. It is assumed that the random vectors are high-dimensional and are multivariate Gaussian distributed. The test employs a family of novel local and global summary statistics generated from small samples of the random vectors. Delay and false alarm analysis of the test is obtained and numerical results are provided to show that the test is consistent in identifying hubs, as the false alarm rate goes to zero.

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arXiv2016

Minimax Optimality of Shiryaev-Roberts Procedure for Quickest Drift Change Detection of a Brownian motion

The problem of detecting a change in the drift of a Brownian motion is considered. The change point is assumed to have a modified exponential prior distribution with unknown parameters. A worst-case analysis with respect to these parameters is adopted leading to a min-max problem formulation. Analytical and numerical justifications are provided towards establishing that the Shiryaev-Roberts procedure with a specially designed starting point is exactly optimal for the proposed mathematical setup.

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arXiv2015

Non-parametric Quickest Change Detection for Large Scale Random Matrices

The problem of quickest detection of a change in the distribution of a $n\times p$ random matrix based on a sequence of observations having a single unknown change point is considered. The forms of the pre- and post-change distributions of the rows of the matrices are assumed to belong to the family of elliptically contoured densities with sparse dispersion matrices but are otherwise unknown. We propose a non-parametric stopping rule that is based on a novel summary statistic related to k-nearest neighbor correlation between columns of each observed random matrix. In the large scale regime of $p\rightarrow \infty$ and $n$ fixed we show that, among all functions of the proposed summary statistic, the proposed stopping rule is asymptotically optimal under a minimax quickest change detection (QCD) model.

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