arXiv subjects

Rahul Singh

Publications and source records attributed to Rahul Singh.

At least 91 records · Page 5Linked to original sources

arXiv2024

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is inevitable, we formulate a semiparametric model of causal inference with high dimensional corrupted data. We propose a procedure for data cleaning, estimation, and inference with data cleaning-adjusted confidence intervals. We prove consistency and Gaussian approximation by finite sample arguments, with a rate of $n^{ 1/2}$ for semiparametric estimands that degrades gracefully for nonparametric estimands. Our key assumption is that the true covariates are approximately low rank, which we interpret as approximate repeated measurements and empirically validate. Our analysis provides nonasymptotic theoretical contributions to matrix completion, statistical learning, and semiparametric statistics. Calibrated simulations verify the coverage of our data cleaning adjusted confidence intervals and demonstrate the relevance of our results for Census-derived data.

econ.EM↗

arXiv2024

On Learning for Ambiguous Chance Constrained Problems

We study chance constrained optimization problems $\min_x f(x)$ s.t. $P(\left\{ θ: g(x,θ)\le 0 \right\})\ge 1-ε$ where $ε\in (0,1)$ is the violation probability, when the distribution $P$ is not known to the decision maker (DM). When the DM has access to a set of distributions $\mathcal{U}$ such that $P$ is contained in $\mathcal{U}$, then the problem is known as the ambiguous chance-constrained problem \cite{erdougan2006ambiguous}. We study ambiguous chance-constrained problem for the case when $\mathcal{U}$ is of the form $\left\{μ:\frac{μ(y)}{ν(y)}\leq C, \forall y\inΘ, μ(y)\ge 0\right\}$, where $ν$ is a ``reference distribution.'' We show that in this case the original problem can be ``well-approximated'' by a sampled problem in which $N$ i.i.d. samples of $θ$ are drawn from $ν$, and the original constraint is replaced with $g(x,θ_i)\le 0,~i=1,2,\ldots,N$. We also derive the sample complexity associated with this approximation, i.e., for $ε,δ>0$ the number of samples which must be drawn from $ν$ so that with a probability greater than $1-δ$ (over the randomness of $ν$), the solution obtained by solving the sampled program yields an $ε$-feasible solution for the original chance constrained problem.

cs.LG↗

arXiv2024

OpineBot: Class Feedback Reimagined Using a Conversational LLM

Conventional class feedback systems often fall short, relying on static, unengaging surveys offering little incentive for student participation. To address this, we present OpineBot, a novel system employing large language models (LLMs) to conduct personalized, conversational class feedback via chatbot interface. We assessed OpineBot's effectiveness in a user study with 20 students from an Indian university's Operating-Systems class, utilizing surveys and interviews to analyze their experiences. Findings revealed a resounding preference for OpineBot compared to conventional methods, highlighting its ability to engage students, produce deeper feedback, offering a dynamic survey experience. This research represents a work in progress, providing early results, marking a significant step towards revolutionizing class feedback through LLM-based technology, promoting student engagement, and leading to richer data for instructors. This ongoing research presents preliminary findings and marks a notable advancement in transforming classroom feedback using LLM-based technology to enhance student engagement and generate comprehensive data for educators.

cs.HC↗

arXiv2023

Related Rhythms: Recommendation System To Discover Music You May Like

Machine Learning models are being utilized extensively to drive recommender systems, which is a widely explored topic today. This is especially true of the music industry, where we are witnessing a surge in growth. Besides a large chunk of active users, these systems are fueled by massive amounts of data. These large-scale systems yield applications that aim to provide a better user experience and to keep customers actively engaged. In this paper, a distributed Machine Learning (ML) pipeline is delineated, which is capable of taking a subset of songs as input and producing a new subset of songs identified as being similar to the inputted subset. The publicly accessible Million Songs Dataset (MSD) enables researchers to develop and explore reasonably efficient systems for audio track analysis and recommendations, without having to access a commercialized music platform. The objective of the proposed application is to leverage an ML system trained to optimally recommend songs that a user might like.

cs.IR↗

arXiv2023

Characteristic cycles of IH sheaves of simply laced minuscule Schubert varieties are irreducible

Let $G/P$ be a complex cominuscule flag manifold of type $E_6,E_7$. We prove that each characteristic cycle of the intersection homology (IH) complex of a Schubert variety in $G/P$ is irreducible. The proof utilizes an earlier algorithm by the same authors which calculates local Euler obstructions, then proceeds by direct computer calculation using Sage. This completes to the exceptional Lie types the characterization of irreducibility of IH sheaves of Schubert varieties in cominuscule $G/P$ obtained by Boe and Fu. As a by-product, we also obtain that the Mather classes, and the Chern-Schwartz-MacPherson classes of Schubert cells in cominuscule $G/P$ of type $E_6,E_7$, are strongly positive.

math.AG↗

arXiv2023

Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputs

Minimum variance controllers have been employed in a wide-range of industrial applications. A key challenge experienced by many adaptive controllers is their poor empirical performance in the initial stages of learning. In this paper, we address the problem of initializing them so that they provide acceptable transients, and also provide an accompanying finite-time regret analysis, for adaptive minimum variance control of an auto-regressive system with exogenous inputs (ARX). Following [3], we consider a modified version of the Certainty Equivalence (CE) adaptive controller, which we call PIECE, that utilizes probing inputs for exploration. We show that it has a $C \log T$ bound on the regret after $T$ time-steps for bounded noise, and $C\log^2 T$ in the case of sub-Gaussian noise. The simulation results demonstrate the advantage of PIECE over the algorithm proposed in [3] as well as the standard Certainty Equivalence controller especially in the initial learning phase. To the best of our knowledge, this is the first work that provides finite-time regret bounds for an adaptive minimum variance controller.

eess.SY↗

arXiv2023

Optimal Scheduling Policies for Remote Estimation of Autoregressive Markov Processes over Time-Correlated Fading Channel

We consider the problem of transmission scheduling for the remote estimation of a discrete-time autoregressive Markov process that is driven by white Gaussian noise. A sensor observes this process, and then decides to either encode the current state of this process into a data packet and attempts to transmit it to the estimator over an unreliable wireless channel modeled as a Gilbert-Elliott channel, or does not send any update. Each transmission attempt consumes $λ$ units of transmission power, and the remote estimator is assumed to be linear. The channel state is revealed only via the feedback (ACK\slash NACK) of a transmission, and hence the channel state is not revealed if no transmission occurs. The goal of the scheduler is to minimize the expected value of an infinite-horizon cumulative discounted cost, in which the instantaneous cost is composed of the following two quantities: (i)~squared estimation error, (ii) transmission power. We show that this problem can equivalently be posed as a partially observable Markov decision process (POMDP), in which the scheduler maintains a belief about the current state of the channel, and makes decisions on the basis of the current value of the estimation error, and the belief state.~We then show that the optimal policy is of threshold-type, i.e. for each value of the estimation error $e$, there is a threshold $b\ust(e)$ such that when the error is equal to $e$, then it is optimal to transmit only when the current belief state is greater than $b\ust(e)$.

math.OC↗

arXiv2023

Augmented RBMLE-UCB Approach for Adaptive Control of Linear Quadratic Systems

We consider the problem of controlling an unknown stochastic linear system with quadratic costs - called the adaptive LQ control problem. We re-examine an approach called ''Reward Biased Maximum Likelihood Estimate'' (RBMLE) that was proposed more than forty years ago, and which predates the ''Upper Confidence Bound'' (UCB) method as well as the definition of ''regret'' for bandit problems. It simply added a term favoring parameters with larger rewards to the criterion for parameter estimation. We show how the RBMLE and UCB methods can be reconciled, and thereby propose an Augmented RBMLE-UCB algorithm that combines the penalty of the RBMLE method with the constraints of the UCB method, uniting the two approaches to optimism in the face of uncertainty. We establish that theoretically, this method retains $\Tilde{\mathcal{O}}(\sqrt{T})$ regret, the best-known so far. We further compare the empirical performance of the proposed Augmented RBMLE-UCB and the standard RBMLE (without the augmentation) with UCB, Thompson Sampling, Input Perturbation, Randomized Certainty Equivalence and StabL on many real-world examples including flight control of Boeing 747 and Unmanned Aerial Vehicle. We perform extensive simulation studies showing that the Augmented RBMLE consistently outperforms UCB, Thompson Sampling and StabL by a huge margin, while it is marginally better than Input Perturbation and moderately better than Randomized Certainty Equivalence.

math.OC↗

arXiv2023

Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments

Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regression for learning nonparametric treatment effects with negative controls. Examples include dose response curves, dose response curves with distribution shift, and heterogeneous treatment effects. Data may be discrete or continuous, and low, high, or infinite dimensional. I prove uniform consistency and provide finite sample rates of convergence. I estimate the dose response curve of cigarette smoking on infant birth weight adjusting for unobserved confounding due to household income, using a data set of singleton births in the state of Pennsylvania between 1989 and 1991.

stat.ML↗

arXiv2023

Whittle Index based Q-Learning for Wireless Edge Caching with Linear Function Approximation

We consider the problem of content caching at the wireless edge to serve a set of end users via unreliable wireless channels so as to minimize the average latency experienced by end users due to the constrained wireless edge cache capacity. We formulate this problem as a Markov decision process, or more specifically a restless multi-armed bandit problem, which is provably hard to solve. We begin by investigating a discounted counterpart, and prove that it admits an optimal policy of the threshold-type. We then show that this result also holds for average latency problem. Using this structural result, we establish the indexability of our problem, and employ the Whittle index policy to minimize average latency. Since system parameters such as content request rates and wireless channel conditions are often unknown and time-varying, we further develop a model-free reinforcement learning algorithm dubbed as Q^{+}-Whittle that relies on Whittle index policy. However, Q^{+}-Whittle requires to store the Q-function values for all state-action pairs, the number of which can be extremely large for wireless edge caching. To this end, we approximate the Q-function by a parameterized function class with a much smaller dimension, and further design a Q^{+}-Whittle algorithm with linear function approximation, which is called Q^{+}-Whittle-LFA. We provide a finite-time bound on the mean-square error of Q^{+}-Whittle-LFA. Simulation results using real traces demonstrate that Q^{+}-Whittle-LFA yields excellent empirical performance.

cs.NI↗

arXiv2022

Double Robustness for Complier Parameters and a Semiparametric Test for Complier Characteristics

We propose a semiparametric test to evaluate (i) whether different instruments induce subpopulations of compliers with the same observable characteristics on average, and (ii) whether compliers have observable characteristics that are the same as the full population on average. The test is a flexible robustness check for the external validity of instruments. We use it to reinterpret the difference in LATE estimates that Angrist and Evans (1998) obtain when using different instrumental variables. To justify the test, we characterize the doubly robust moment for Abadie (2003)'s class of complier parameters, and we analyze a machine learning update to $κ$ weighting.

stat.ML↗

arXiv2022

DEEPFAKE CLI: Accelerated Deepfake Detection using FPGAs

Because of the availability of larger datasets and recent improvements in the generative model, more realistic Deepfake videos are being produced each day. People consume around one billion hours of video on social media platforms every day, and thats why it is very important to stop the spread of fake videos as they can be damaging, dangerous, and malicious. There has been a significant improvement in the field of deepfake classification, but deepfake detection and inference have remained a difficult task. To solve this problem in this paper, we propose a novel DEEPFAKE C-L-I (Classification-Localization-Inference) in which we have explored the idea of accelerating Quantized Deepfake Detection Models using FPGAs due to their ability of maximum parallelism and energy efficiency compared to generalized GPUs. In this paper, we have used light MesoNet with EFF-YNet structure and accelerated it on VCK5000 FPGA, powered by state-of-the-art VC1902 Versal Architecture which uses AI, DSP, and Adaptable Engines for acceleration. We have benchmarked our inference speed with other state-of-the-art inference nodes, got 316.8 FPS on VCK5000 while maintaining 93\% Accuracy.

cs.AR↗

arXiv2022

Inverse modeling of circular lattices via orbit response measurements in the presence of degeneracy

The number and relative placement of BPMs and steerers with respect to the quadrupoles in a circular lattice can lead to degeneracy in the context of inverse modeling of accelerator optics. Further, the measurement uncertainties introduced by beam position monitors can propagate by the inverse modeling process in ways that prohibit the successful estimation of model errors. In this contribution, the influence of BPM and steerer placement on the conditioning of the inverse problem is studied. An analytical version of the Jacobian, linking the quadrupole gradient errors along with BPM and steerer gain errors with the orbit response matrix, is derived. It is demonstrated that this analytical version of the Jacobian can be used in place of the numerically obtained Jacobian during the fitting procedure. The approach is first tested with simulations and the findings are verified by measurement data taken on SIS18 synchrotron at GSI. The results are crosschecked with the standard numerical Jacobian approach. The quadrupole errors causing tune discrepancies observed at SIS18 are identified.

physics.acc-ph↗

arXiv2022

De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers

We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ``double sparsity robustness'': either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse''. Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.

stat.ML↗

arXiv2022

Automatic Debiased Machine Learning of Causal and Structural Effects

Many causal and structural effects depend on regressions. Examples include policy effects, average derivatives, regression decompositions, average treatment effects, causal mediation, and parameters of economic structural models. The regressions may be high dimensional, making machine learning useful. Plugging machine learners into identifying equations can lead to poor inference due to bias from regularization and/or model selection. This paper gives automatic debiasing for linear and nonlinear functions of regressions. The debiasing is automatic in using Lasso and the function of interest without the full form of the bias correction. The debiasing can be applied to any regression learner, including neural nets, random forests, Lasso, boosting, and other high dimensional methods. In addition to providing the bias correction we give standard errors that are robust to misspecification, convergence rates for the bias correction, and primitive conditions for asymptotic inference for estimators of a variety of estimators of structural and causal effects. The automatic debiased machine learning is used to estimate the average treatment effect on the treated for the NSW job training data and to estimate demand elasticities from Nielsen scanner data while allowing preferences to be correlated with prices and income.

math.ST↗

arXiv2022

Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves

We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a decomposition property specific to the RKHS, our estimators have simple closed form solutions. We prove uniform consistency with finite sample rates via original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training program for disadvantaged youths.

econ.EM↗

arXiv2022

A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees

Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is $n^{-1/2}$ for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for ill posed inverse problems.

stat.ML↗

arXiv2022

Signed Graph Neural Networks: A Frequency Perspective

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each convolution layer they perform low-pass filtering of the input features followed by a learnable linear transformation. Their extension to signed graphs with positive as well as negative links imposes multiple issues including computational irregularities and ambiguous frequency interpretation, making the design of computationally efficient low pass filters challenging. In this paper, we address these issues via spectral analysis of signed graphs and propose two different signed graph neural networks, one keeps only low-frequency information and one also retains high-frequency information. We further introduce magnetic signed Laplacian and use its eigendecomposition for spectral analysis of directed signed graphs. We test our methods for node classification and link sign prediction tasks on signed graphs and achieve state-of-the-art performances.

cs.LG↗