arXiv subjects

Samarjit Das

Publications and source records attributed to Samarjit Das.

15 recordsLinked to original sources

arXiv2026

Estimation of multiple precision matrices under shared support with heterogeneous edge strengths

Estimating multiple precision matrices in high-dimension presents significant challenges, particularly when distinct datasets share a common conditional dependency structure but exhibit population-specific interaction strengths. We address this problem by introducing the Multiplicative Graphical Lasso (Mglasso), a method for jointly estimating precision matrices across multiple Gaussian graphical models under a shared sparsity constraint. Each precision matrix is decomposed as a Schur-Hadamard product of a shared structural matrix $\boldsymbol{\Theta}$, which encodes the common conditional independence graph, and a population-specific matrix $\boldsymbol{\Gamma}_{l}$, which captures variation in edge strengths across populations. We optimize a penalized log-likelihood that utilizes an $\ell_1$-penalty to enforce common sparsity and a Frobenius norm penalty to regulate population-specific variations. The optimization is efficiently performed using the Alternating Direction Method of Multipliers (ADMM) algorithm integrated with gradient descent. Theoretically, we establish the local strict convexity of the objective function and provide rigorous high-dimensional consistency guarantees, including supremum norm error bounds and exact support recovery under sub-Gaussian tail conditions. Extensive simulations show superior model selection consistency at smaller sample sizes compared to the benchmark Group Graphical Lasso (GGL). Finally, the method's practical utility is further validated through real-world applications.

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arXiv2026

Linear Regression: Inference Based on Cluster Estimates

This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite cluster sizes. The analysis is then extended to a standard random coefficient model, where we derive asymptotic results for the average (common) parameters and develop a Wald-type test for general linear hypotheses. We also investigate the performance of the conventional pooled ordinary least squares (POLS) estimator within the random coefficients framework and show that it can be unreliable across a wide range of empirically relevant settings. Furthermore, we introduce a new test for parameter stability at a higher (superblock; Tier 2, Tier 3,...) level, assuming that parameters are stable across clusters within that level. Extensive simulation studies demonstrate the effectiveness of the proposed tests, and an empirical application illustrates their practical relevance.

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arXiv2025

Statistical inference using debiased group graphical lasso for multiple sparse precision matrices

Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates and model selection consistency under irrepresentability conditions. Based on these results, we construct debiased estimators that are asymptotically Gaussian, allowing hypothesis testing for linear combinations of precision matrix entries across populations. We also investigate regimes where irrepresentibility conditions does not hold, showing that consistency can still be attained in moderately high-dimensional settings. Simulation studies confirm the theoretical results, and applications to real datasets demonstrate the practical utility of the method.

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arXiv2024

Cross Sectional Regression with Cluster Dependence: Inference based on Averaging

We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, $\hat{\beta} _P$, in the context of cluster dependence. The present study considers various scenarios under various restrictions on the cluster sizes and number of clusters. It is shown that $\hat{\beta}_P$ could be inconsistent in many realistic situations. We propose a simple estimator, $\hat{\beta}_A$ based on data averaging. The asymptotic properties of $\hat{\beta}_A$ are studied. It is shown that $\hat{\beta}_A$ is consistent even when $\hat{\beta}_P$ is inconsistent. It is further shown that the proposed estimator $\hat{\beta}_A$ is more efficient than $\hat{\beta}_P$ in many practical scenarios. As a consequence of averaging, we show that $\hat{\beta}_A$ retains consistency, asymptotic normality under classical measurement error problem circumventing the use of Instrumental Variables (IV). A detailed simulation study shows the efficacy of $\hat{\beta}_A$. It is also seen that $\hat{\beta}_A$ yields better goodness of fit.

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arXiv2022

Learning to Adapt to Domain Shifts with Few-shot Samples in Anomalous Sound Detection

Anomaly detection has many important applications, such as monitoring industrial equipment. Despite recent advances in anomaly detection with deep-learning methods, it is unclear how existing solutions would perform under out-of-distribution scenarios, e.g., due to shifts in machine load or environmental noise. Grounded in the application of machine health monitoring, we propose a framework that adapts to new conditions with few-shot samples. Building upon prior work, we adopt a classification-based approach for anomaly detection and show its equivalence to mixture density estimation of the normal samples. We incorporate an episodic training procedure to match the few-shot setting during inference. We define multiple auxiliary classification tasks based on meta-information and leverage gradient-based meta-learning to improve generalization to different shifts. We evaluate our proposed method on a recently-released dataset of audio measurements from different machine types. It improved upon two baselines by around 10% and is on par with best-performing model reported on the dataset.

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arXiv2021

Identifying Actions for Sound Event Classification

In Psychology, actions are paramount for humans to identify sound events. In Machine Learning (ML), action recognition achieves high accuracy; however, it has not been asked whether identifying actions can benefit Sound Event Classification (SEC), as opposed to mapping the audio directly to a sound event. Therefore, we propose a new Psychology-inspired approach for SEC that includes identification of actions via human listeners. To achieve this goal, we used crowdsourcing to have listeners identify 20 actions that in isolation or in combination may have produced any of the 50 sound events in the well-studied dataset ESC-50. The resulting annotations for each audio recording relate actions to a database of sound events for the first time. The annotations were used to create semantic representations called Action Vectors (AVs). We evaluated SEC by comparing the AVs with two types of audio features -- log-mel spectrograms and state-of-the-art audio embeddings. Because audio features and AVs capture different abstractions of the acoustic content, we combined them and achieved one of the highest reported accuracies (88%).

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arXiv2019

Relative Efficiency of Higher Normed Estimators Over the Least Squares Estimator

In this article, we study the performance of the estimator that minimizes $L_{2k}- $ order loss function (for $ k \ge \; 2 )$ against the estimators which minimizes the $L_2-$ order loss function (or the least squares estimator). Commonly occurring examples illustrate the differences in efficiency between $L_{2k}$ and $L_2 -$ based estimators. We derive an empirically testable condition under which the $L_{2k}$ estimator is more efficient than the least squares estimator. We construct a simple decision rule to choose between $L_{2k}$ and $L_2$ estimator. Special emphasis is provided to study $L_{4}$ estimator. A detailed simulation study verifies the effectiveness of this decision rule. Also, the superiority of the $L_{2k}$ estimator is demonstrated in a real life data set.

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arXiv2018

Understanding Cross-sectional Dependence in Panel Data

We provide various norm-based definitions of different types of cross-sectional dependence and the relations between them. These definitions facilitate to comprehend and to characterize the various forms of cross-sectional dependence, such as strong, semi-strong, and weak dependence. Then we examine the asymptotic properties of parameter estimators both for fixed (within) effect estimator and random effect (pooled) estimator for linear panel data models incorporating various forms of cross-sectional dependence. The asymptotic properties are also derived when both cross-sectional and temporal dependence are present. Subsequently, we develop consistent and robust standard error of the parameter estimators both for fixed effect and random effect model separately. Robust standard errors are developed (i) for pure cross-sectional dependence; and (ii) also for cross-sectional and time series dependence. Under strong or semi-strong cross-sectional dependence, it is established that when the time dependence comes through the idiosyncratic errors, such time dependence does not have any influence in the asymptotic variance of $(\hat{\beta}_{FE/RE}). $ Hence, it is argued that in estimating $Var(\hat{\beta}_{FE/RE}),$ Newey-West kind of correction injects bias in the variance estimate. Furthermore, this article lay down conditions under which $t$, $F$ and the $Wald$ statistics based on the robust covariance matrix estimator give valid inference.

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arXiv2017

Eventness: Object Detection on Spectrograms for Temporal Localization of Audio Events

In this paper, we introduce the concept of Eventness for audio event detection, which can, in part, be thought of as an analogue to Objectness from computer vision. The key observation behind the eventness concept is that audio events reveal themselves as 2-dimensional time-frequency patterns with specific textures and geometric structures in spectrograms. These time-frequency patterns can then be viewed analogously to objects occurring in natural images (with the exception that scaling and rotation invariance properties do not apply). With this key observation in mind, we pose the problem of detecting monophonic or polyphonic audio events as an equivalent visual object(s) detection problem under partial occlusion and clutter in spectrograms. We adapt a state-of-the-art visual object detection model to evaluate the audio event detection task on publicly available datasets. The proposed network has comparable results with a state-of-the-art baseline and is more robust on minority events. Provided large-scale datasets, we hope that our proposed conceptual model of eventness will be beneficial to the audio signal processing community towards improving performance of audio event detection.

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arXiv2017

Multiple Instance Deep Learning for Weakly Supervised Small-Footprint Audio Event Detection

State-of-the-art audio event detection (AED) systems rely on supervised learning using strongly labeled data. However, this dependence severely limits scalability to large-scale datasets where fine resolution annotations are too expensive to obtain. In this paper, we propose a small-footprint multiple instance learning (MIL) framework for multi-class AED using weakly annotated labels. The proposed MIL framework uses audio embeddings extracted from a pre-trained convolutional neural network as input features. We show that by using audio embeddings the MIL framework can be implemented using a simple DNN with performance comparable to recurrent neural networks. We evaluate our approach by training an audio tagging system using a subset of AudioSet, which is a large collection of weakly labeled YouTube video excerpts. Combined with a late-fusion approach, we improve the F1 score of a baseline audio tagging system by 17%. We show that audio embeddings extracted by the convolutional neural networks significantly boost the performance of all MIL models. This framework reduces the model complexity of the AED system and is suitable for applications where computational resources are limited.

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arXiv2017

A Light-Weight Multimodal Framework for Improved Environmental Audio Tagging

The lack of strong labels has severely limited the state-of-the-art fully supervised audio tagging systems to be scaled to larger dataset. Meanwhile, audio-visual learning models based on unlabeled videos have been successfully applied to audio tagging, but they are inevitably resource hungry and require a long time to train. In this work, we propose a light-weight, multimodal framework for environmental audio tagging. The audio branch of the framework is a convolutional and recurrent neural network (CRNN) based on multiple instance learning (MIL). It is trained with the audio tracks of a large collection of weakly labeled YouTube video excerpts; the video branch uses pretrained state-of-the-art image recognition networks and word embeddings to extract information from the video track and to map visual objects to sound events. Experiments on the audio tagging task of the DCASE 2017 challenge show that the incorporation of video information improves a strong baseline audio tagging system by 5.3\% absolute in terms of $F_1$ score. The entire system can be trained within 6~hours on a single GPU, and can be easily carried over to other audio tasks such as speech sentimental analysis.

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arXiv2017

A Comparison of deep learning methods for environmental sound

Environmental sound detection is a challenging application of machine learning because of the noisy nature of the signal, and the small amount of (labeled) data that is typically available. This work thus presents a comparison of several state-of-the-art Deep Learning models on the IEEE challenge on Detection and Classification of Acoustic Scenes and Events (DCASE) 2016 challenge task and data, classifying sounds into one of fifteen common indoor and outdoor acoustic scenes, such as bus, cafe, car, city center, forest path, library, train, etc. In total, 13 hours of stereo audio recordings are available, making this one of the largest datasets available. We perform experiments on six sets of features, including standard Mel-frequency cepstral coefficients (MFCC), Binaural MFCC, log Mel-spectrum and two different large- scale temporal pooling features extracted using OpenSMILE. On these features, we apply five models: Gaussian Mixture Model (GMM), Deep Neural Network (DNN), Recurrent Neural Network (RNN), Convolutional Deep Neural Net- work (CNN) and i-vector. Using the late-fusion approach, we improve the performance of the baseline 72.5% by 15.6% in 4-fold Cross Validation (CV) avg. accuracy and 11% in test accuracy, which matches the best result of the DCASE 2016 challenge. With large feature sets, deep neural network models out- perform traditional methods and achieve the best performance among all the studied methods. Consistent with other work, the best performing single model is the non-temporal DNN model, which we take as evidence that sounds in the DCASE challenge do not exhibit strong temporal dynamics.

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arXiv2016

Understanding Audio Pattern Using Convolutional Neural Network From Raw Waveforms

One key step in audio signal processing is to transform the raw signal into representations that are efficient for encoding the original information. Traditionally, people transform the audio into spectral representations, as a function of frequency, amplitude and phase transformation. In this work, we take a purely data-driven approach to understand the temporal dynamics of audio at the raw signal level. We maximize the information extracted from the raw signal through a deep convolutional neural network (CNN) model. Our CNN model is trained on the urbansound8k dataset. We discover that salient audio patterns embedded in the raw waveforms can be efficiently extracted through a combination of nonlinear filters learned by the CNN model.

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arXiv2016

Learning Filter Banks Using Deep Learning For Acoustic Signals

Designing appropriate features for acoustic event recognition tasks is an active field of research. Expressive features should both improve the performance of the tasks and also be interpret-able. Currently, heuristically designed features based on the domain knowledge requires tremendous effort in hand-crafting, while features extracted through deep network are difficult for human to interpret. In this work, we explore the experience guided learning method for designing acoustic features. This is a novel hybrid approach combining both domain knowledge and purely data driven feature designing. Based on the procedure of log Mel-filter banks, we design a filter bank learning layer. We concatenate this layer with a convolutional neural network (CNN) model. After training the network, the weight of the filter bank learning layer is extracted to facilitate the design of acoustic features. We smooth the trained weight of the learning layer and re-initialize it in filter bank learning layer as audio feature extractor. For the environmental sound recognition task based on the Urban- sound8K dataset, the experience guided learning leads to a 2% accuracy improvement compared with the fixed feature extractors (the log Mel-filter bank). The shape of the new filter banks are visualized and explained to prove the effectiveness of the feature design process.

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arXiv2016

Very Deep Convolutional Neural Networks for Raw Waveforms

Learning acoustic models directly from the raw waveform data with minimal processing is challenging. Current waveform-based models have generally used very few (~2) convolutional layers, which might be insufficient for building high-level discriminative features. In this work, we propose very deep convolutional neural networks (CNNs) that directly use time-domain waveforms as inputs. Our CNNs, with up to 34 weight layers, are efficient to optimize over very long sequences (e.g., vector of size 32000), necessary for processing acoustic waveforms. This is achieved through batch normalization, residual learning, and a careful design of down-sampling in the initial layers. Our networks are fully convolutional, without the use of fully connected layers and dropout, to maximize representation learning. We use a large receptive field in the first convolutional layer to mimic bandpass filters, but very small receptive fields subsequently to control the model capacity. We demonstrate the performance gains with the deeper models. Our evaluation shows that the CNN with 18 weight layers outperform the CNN with 3 weight layers by over 15% in absolute accuracy for an environmental sound recognition task and matches the performance of models using log-mel features.

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