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In the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items in the pool belonging to each category. A prominent special case is quantitative group testing (QGT), which is the case of pooled data with two categories. We consider these problems in the non-adaptive and linear regime, where the fraction of items in each category is of constant order. We propose a scheme with a spatially coupled Bernoulli test matrix and an efficient approximate message passing (AMP) algorithm for recovery. We rigorously characterize its asymptotic performance in both the noiseless and noisy settings, and prove that in the noiseless case, the AMP algorithm achieves almost-exact recovery with a number of tests sublinear in the number of items. For both QGT and pooled data, this is the first efficient scheme that provably achieves recovery in the linear regime with a sublinear number of tests, with performance degrading gracefully in the presence of noise. Numerical simulations illustrate the benefits of the spatially coupled scheme at finite dimensions, showing that it outperforms i.i.d. test designs as well as other recovery algorithms based on convex programming., Comment: 49 pages, 6 figures

First time in six decades, uncountable infinite exact solutions of FitzHugh-Nagumo model with diffusion have been found. FitzHugh-Nagumo model is a nonlinear dynamical system applicable to neurosciences, chemical kinetics, cell division, population dynamics, electronics, epidemiology, cardiac physiology and pattern formation. Non-classical symmetry analysis has been carried out to find invariant solutions. In many ways this finding makes the corpus of asymptotics and numerics obsolete. Non singular, physically stable and meaningful solutions could now be found without distorting the actual model or introducing forced conditions.

This research combines MediaPipe and CNNs for the efficient and accurate interpretation of ASL dataset for the real-time detection of sign language. The system presented here captures and processes hands' gestures in real time. the intended purpose was to create a very easy, accurate, and fast way of entering commands without the necessity of touching something.MediaPipe supports one of the powerful frameworks in real-time hand tracking capabilities for the ability to capture and preprocess hand movements, which increases the accuracy of the gesture recognition system. Actually, the integration of CNN with the MediaPipe results in higher efficiency in using the model of real-time processing.The accuracy achieved by the model on ASL datasets is 99.12\%.The model was tested using American Sign Language (ASL) datasets. The results were then compared to those of existing methods to evaluate how well it performed, using established evaluation techniques. The system will have applications in the communication, education, and accessibility domains. Making systems such as described in this paper even better will assist people with hearing impairment and make things accessible to them. We tested the recognition and translation performance on an ASL dataset and achieved better accuracy over previous models.It is meant to the research is to identify the characters that American signs recognize using hand images taken from a web camera by based on mediapipe and CNNs, Comment: We have decided to withdraw our paper due to significant revisions and improvements that need to be made based on new findings. After further analysis, we believe these changes are necessary to ensure the accuracy and completeness of our work. We plan to resubmit the revised version in the future once the updates are complete

We consider the problem of localizing change points in a generalized linear model (GLM), a model that covers many widely studied problems in statistical learning including linear, logistic, and rectified linear regression. We propose a novel and computationally efficient Approximate Message Passing (AMP) algorithm for estimating both the signals and the change point locations, and rigorously characterize its performance in the high-dimensional limit where the number of parameters $p$ is proportional to the number of samples $n$. This characterization is in terms of a state evolution recursion, which allows us to precisely compute performance measures such as the asymptotic Hausdorff error of our change point estimates, and allows us to tailor the algorithm to take advantage of any prior structural information on the signals and change points. Moreover, we show how our AMP iterates can be used to efficiently compute a Bayesian posterior distribution over the change point locations in the high-dimensional limit. We validate our theory via numerical experiments, and demonstrate the favorable performance of our estimators on both synthetic and real data in the settings of linear, logistic, and rectified linear regression., Comment: 43 pages, 9 figures. A preliminary version of this paper appeared in ICML 2024

It is often desirable for Large Language Models (LLMs) to capture multiple objectives when providing a response. In document-grounded response generation, for example, agent responses are expected to be relevant to a user's query while also being grounded in a given document. In this paper, we introduce Proxy Metric-based Self-Refinement (ProMiSe), which enables an LLM to refine its own initial response along key dimensions of quality guided by external metrics feedback, yielding an overall better final response. ProMiSe leverages feedback on response quality through principle-specific proxy metrics, and iteratively refines its response one principle at a time. We apply ProMiSe to open source language models Flan-T5-XXL and Llama-2-13B-Chat, to evaluate its performance on document-grounded question answering datasets, MultiDoc2Dial and QuAC, demonstrating that self-refinement improves response quality. We further show that fine-tuning Llama-2-13B-Chat on the synthetic dialogue data generated by ProMiSe yields significant performance improvements over the zero-shot baseline as well as a supervised fine-tuned model on human annotated data.

We consider communication over the Gaussian multiple-access channel in the regime where the number of users grows linearly with the codelength. In this regime, schemes based on sparse superposition coding can achieve a near-optimal tradeoff between spectral efficiency and signal-to-noise ratio. However, these schemes are feasible only for small values of user payload. This paper investigates efficient schemes for larger user payloads, focusing on coded CDMA schemes where each user's information is encoded via a linear code before being modulated with a signature sequence. We propose an efficient approximate message passing (AMP) decoder that can be tailored to the structure of the linear code, and provide an exact asymptotic characterization of its performance. Based on this result, we consider a decoder that integrates AMP and belief propagation and characterize its tradeoff between spectral efficiency and signal-to-noise ratio, for a given target error rate. Simulation results show that the decoder achieves state-of-the-art performance at finite lengths, with a coded CDMA scheme defined using LDPC codes and a spatially coupled matrix of signature sequences., Comment: 25 pages, 8 figures. A shorter version of this paper appeared in the Proceedings of IEEE ISIT 2024

Strong policies with sustainable incentives are needed to accelerate the EV transition. This paper assesses various feebate designs assessing recent policy evolution in five European countries. While there are key design elements that should be considered, there is no optimal feebate design. Different policy objectives could be served by feebates influencing its design and effectiveness. Using feebates to transition to EVs has emerged a key objective. With the financial sustainability of EV incentive programs being questioned, a self financing market mechanism could be the need of the hour solution. Irrespective of the policy goals, a feebate will impact both the supply side, i.e., the automotive industry and the consumer side. Globally, feebates can be used to effect technology leapfrogging while navigating the political economy of clean transportation policy in different country contexts. This paper highlights thirteen design elements of an effective feebate policy that can serve as a foundation for policymakers.

In the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items of each category within the pool. We study an approximate message passing (AMP) algorithm for estimating the categories and rigorously characterize its performance, in both the noiseless and noisy settings. For the noiseless setting, we show that the AMP algorithm is equivalent to one recently proposed by El Alaoui et al. Our results provide a rigorous version of their performance guarantees, previously obtained via non-rigorous techniques. For the case of pooled data with two categories, known as quantitative group testing (QGT), we use the AMP guarantees to compute precise limiting values of the false positive rate and the false negative rate. Though the pooled data problem and QGT are both instances of estimation in a linear model, existing AMP theory cannot be directly applied since the design matrices are binary valued. The key technical ingredient in our analysis is a rigorous asymptotic characterization of AMP for generalized linear models defined via generalized white noise design matrices. This result, established using a recent universality result of Wang et al., is of independent interest. Our theoretical results are validated by numerical simulations. For comparison, we propose estimators based on convex relaxation and iterative thresholding, without providing theoretical guarantees. The simulations indicate that AMP consistently outperforms these estimators., Comment: 62 pages, 11 figures, appeared in SIAM Journal on Mathematics of Data Science. The simulation results here use a slightly different metric from the journal version; see Remark 4.2

We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has precisely characterized the asymptotic minimum mean-squared error (MMSE) for GLMs with i.i.d. Gaussian sensing matrices. However, in many models there is a significant gap between the MMSE and the performance of the best known feasible estimators. In this work, we address this issue by considering GLMs defined via spatially coupled sensing matrices. We propose an efficient approximate message passing (AMP) algorithm for estimation and prove that with a simple choice of spatially coupled design, the MSE of a carefully tuned AMP estimator approaches the asymptotic MMSE in the high-dimensional limit. To prove the result, we first rigorously characterize the asymptotic performance of AMP for a GLM with a generic spatially coupled design. This characterization is in terms of a deterministic recursion (`state evolution') that depends on the parameters defining the spatial coupling. Then, using a simple spatially coupled design and a judicious choice of functions for the AMP algorithm, we analyze the fixed points of the resulting state evolution and show that it achieves the asymptotic MMSE. Numerical results for phase retrieval and rectified linear regression show that spatially coupled designs can yield substantially lower MSE than i.i.d. Gaussian designs at finite dimensions when used with AMP algorithms., Comment: 41 pages, 4 figures. Appeared in the IEEE Transactions on Information Theory

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective solution. However, despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured (i.i.d.\ Gaussian and Haar orthogonal) designs. In contrast, real-world data matrices are highly structured and exhibit non-trivial correlations. To address the problem, we consider correlated Gaussian designs capturing the anisotropic nature of the features via a covariance matrix $\Sigma$. Our main result is a precise asymptotic characterization of the performance of spectral estimators. This allows us to identify the optimal preprocessing that minimizes the number of samples needed for parameter estimation. Surprisingly, such preprocessing is universal across a broad set of designs, which partly addresses a conjecture on optimal spectral estimators for rotationally invariant models. Our principled approach vastly improves upon previous heuristic methods, including for designs common in computational imaging and genetics. The proposed methodology, based on approximate message passing, is broadly applicable and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings.

Global light duty electric vehicle (EV) sales exceeded 10.5 million units in 2022, with a year-on-year growth of 55%, but these trends differ regionally. Despite the robust growth, upfront purchase price remains a challenge for consumers in different regions, and thus, OEMs make technology choices to respond to market needs. This paper examines the electrification portfolio choices of three major automotive manufacturers (OEMs) in different regions of the world, including Europe, Americas, Asia Pacific, and Africa/Middle-East. The analysis focuses on trends in dominant segments for Battery Electric Vehicles (BEV) and Plug-in Hybrid Electric Vehicles (PHEV), as well as battery chemistry choices. Regional differences show a trend towards SUVs for both BEVs and PHEVs. Tesla's dominance in the BEV market influences battery chemistry choices. Average battery sizes for BEVs remain similar in Europe and Americas, but lower in Asia Pacific and Africa/Middle East., Comment: 12 pages, 18 figures, 2 tables

We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear regression, max-affine regression, and mixture-of-experts. In mixed linear regression, each observation comes from one of $L$ signal vectors (regressors), but we do not know which one; in max-affine regression, each observation comes from the maximum of $L$ affine functions, each defined via a different signal vector. The goal in all these problems is to estimate the signals, and possibly some of the latent variables, from the observations. We propose a novel approximate message passing (AMP) algorithm for estimation in a matrix GLM and rigorously characterize its performance in the high-dimensional limit. This characterization is in terms of a state evolution recursion, which allows us to precisely compute performance measures such as the asymptotic mean-squared error. The state evolution characterization can be used to tailor the AMP algorithm to take advantage of any structural information known about the signals. Using state evolution, we derive an optimal choice of AMP `denoising' functions that minimizes the estimation error in each iteration. The theoretical results are validated by numerical simulations for mixed linear regression, max-affine regression, and mixture-of-experts. For max-affine regression, we propose an algorithm that combines AMP with expectation-maximization to estimate intercepts of the model along with the signals. The numerical results show that AMP significantly outperforms other estimators for mixed linear regression and max-affine regression in most parameter regimes., Comment: 44 pages. To appear in the Journal of Machine Learning Research. A shorter version of this paper appeared in the proceedings of AISTATS 2023

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear in the dimension, and additive noise is assumed to be independent Gaussian with variance $\sigma^2$. Prior work has shown that the problem suffers from a $\frac{k}{SNR^2}$-to-$\frac{k^2}{SNR^2}$ statistical-to-computational gap, resembling other computationally challenging high-dimensional inference problems such as Sparse PCA and Robust Sparse Mean Estimation; here $SNR$ is the signal-to-noise ratio. We establish the existence of a more extensive computational barrier for this problem through the method of low-degree polynomials, but show that the problem is computationally hard only in a very narrow symmetric parameter regime. We identify a smooth information-computation tradeoff between the sample complexity $n$ and runtime for any randomized algorithm in this hard regime. Via a simple reduction, this provides novel rigorous evidence for the existence of a computational barrier to solving exact support recovery in sparse phase retrieval with sample complexity $n = \tilde{o}(k^2)$. Our second contribution is to analyze a simple thresholding algorithm which, outside of the narrow regime where the problem is hard, solves the associated mixed regression detection problem in $O(np)$ time with square-root the number of samples and matches the sample complexity required for (non-mixed) sparse linear regression; this allows the recovery problem to be subsequently solved by state-of-the-art techniques from the dense case. As a special case of our results, we show that this simple algorithm is order-optimal among a large family of algorithms in solving exact signed support recovery in sparse linear regression., Comment: To appear in Conference on Learning Theory (COLT) 2023

In this paper, we study gyro-groups associated to groups, group extensions admitting gyro-sections, and corresponding co-homologies. We also describe the obstructions in terms of co-homomology. The notion of gyro-Schur Multiplier and that of gyro-Milnor $K_{2}$ group are introduced., Comment: Accepted in Journal of Algebra and Its Applications