Anubhab Ghosh

Anubhab Ghosh, Antoine Honoré, Saikat Chatterjee

We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. For a model-free process, we do not have any a-priori knowledge of the process dynamics. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), a data-driven deep Markov model (DMM) and a recently proposed hybrid method called KalmanNet. In addition, we show that DANSE works for high-dimensional state estimation.

Anubhab Ghosh, Yonina C. Eldar, Saikat Chatterjee

We consider data-driven Bayesian state estimation from compressed measurements (BSCM) of a model-free process. The dimension of the temporal measurement vector is lower than that of the temporal state vector to be estimated, leading to an under-determined inverse problem. The underlying dynamical model of the state's evolution is unknown for a `model-free process.' Hence, it is difficult to use traditional model-driven methods, for example, Kalman and particle filters. Instead, we consider data-driven methods. We experimentally show that two existing unsupervised learning-based data-driven methods fail to address the BSCM problem in a model-free process. The methods are -- data-driven nonlinear state estimation (DANSE) and deep Markov model (DMM). While DANSE provides good predictive/forecasting performance to model the temporal measurement data as a time series, its unsupervised learning lacks suitable regularization for tackling the BSCM task. We then propose a semi-supervised learning approach and develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE. In SemiDANSE, we use a large amount of unlabelled data along with a limited amount of labelled data, i.e., pairwise measurement-and-state data, which provides the desired regularization. Using {benchmark chaotic dynamical systems}, we {empirically} show that the data-driven SemiDANSE provides competitive state estimation performance for BSCM {using a handful of different measurement systems}, against a hybrid method called KalmanNet and two model-driven methods (extended Kalman filter and unscented Kalman filter) that know the dynamical models exactly.

Anubhab Ghosh, Yonina C. Eldar, Saikat Chatterjee

We consider data-driven Bayesian state estimation from compressed measurements (BSCM) of a model-free process. The dimension of the temporal measurement vector is lower than that of the temporal state vector to be estimated, leading to an under-determined inverse problem. The underlying dynamical model of the state's evolution is unknown for a 'model-free process.' Hence, it is difficult to use traditional model-driven methods, for example, Kalman and particle filters. Instead, we consider data-driven methods. We experimentally show that two existing unsupervised learning-based data-driven methods fail to address the BSCM problem in a model-free process. The methods are -- data-driven nonlinear state estimation (DANSE) and deep Markov model (DMM). While DANSE provides good predictive/forecasting performance to model the temporal measurement data as a time series, its unsupervised learning lacks suitable regularization for tackling the BSCM task. We then propose a semi-supervised learning approach and develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE. In SemiDANSE, we use a large amount of unlabelled data along with a limited amount of labelled data, i.e., pairwise measurement-and-state data, which provides the desired regularization. Using benchmark chaotic dynamical systems, we empirically show that the data-driven SemiDANSE provides competitive state estimation performance for BSCM using a handful of different measurement systems, against a hybrid method called KalmanNet and two model-driven methods (extended Kalman filter and unscented Kalman filter) that know the dynamical models exactly.

Anubhab Ghosh, Mohamed Abdalmoaty, Saikat Chatterjee et al.

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks -- long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.

Anubhab Ghosh, Yonina C. Eldar, Saikat Chatterjee

We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements of a process whose underlying state transition model (STM) is unknown. Such a process is referred to as a model-free process. A recurrent neural network (RNN) provides parameters of a Gaussian prior that characterize the state of the model-free process, using all previous measurements at a given time point. In the case of DANSE, the measurement system was linear, leading to a closed-form solution for the state posterior. However, the presence of a nonlinear measurement system renders a closed-form solution infeasible. Instead, the second-order statistics of the state posterior are computed using the nonlinear measurements observed at the time point. We address the nonlinear measurements using a reparameterization trick-based particle sampling approach, and estimate the second-order statistics of the state posterior. The proposed method is referred to as particle-based DANSE (pDANSE). The RNN of pDANSE uses sequential measurements efficiently and avoids the use of computationally intensive sequential Monte-Carlo (SMC) and/or ancestral sampling. We describe the semi-supervised learning method for pDANSE, which transitions to unsupervised learning in the absence of labeled data. Using a stochastic Lorenz-$63$ system as a benchmark process, we experimentally demonstrate the state estimation performance for four nonlinear measurement systems. We explore cubic nonlinearity and a camera-model nonlinearity where unsupervised learning is used; then we explore half-wave rectification nonlinearity and Cartesian-to-spherical nonlinearity where semi-supervised learning is used. The performance of state estimation is shown to be competitive vis-à-vis particle filters that have complete knowledge of the STM of the Lorenz-$63$ system.

Antoine Honoré, Anubhab Ghosh, Saikat Chatterjee

We consider reconstruction of an ambient signal in a compressed sensing (CS) setup where the ambient signal has a neural network based generative model. The generative model has a sparse-latent input and we refer to the generated ambient signal as generative sparse-latent signal (GSL). The proposed sparsity inducing reconstruction algorithm is inherently non-convex, and we show that a gradient based search provides a good reconstruction performance. We evaluate our proposed algorithm using simulated data.

Gustav Norén, Anubhab Ghosh, Fredrik Cumlin et al.

We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have a suitable physics-based model characterizing the temporal evolution of the process state. The closed-form Gaussian posterior is provided by a recurrent neural network (RNN). The use of RNN is computationally simple in the inference phase. For learning the RNN, an additional RNN is used in the learning phase. Both RNNs help each other learn better based on variational inference principles. The VSE is demonstrated for a tracking application - state estimation of a stochastic Lorenz system (a benchmark process) using a 2-D camera measurement model. The VSE is shown to be competitive against a particle filter that knows the Lorenz system model and a recently proposed data-driven state estimation method that does not know the Lorenz system model.

Fredrik Cumlin, Anubhab Ghosh, Saikat Chatterjee

We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the nonlinear dynamics of the complex process. There is no state-transition model (STM) of the process available. The proposed DNS uses a recurrent architecture that helps to provide a closed-form posterior of the hidden state sequence given the measurement sequence. DNS learns in an unsupervised manner, meaning the training dataset consists of only measurement data and no state data. We demonstrate DNS using simulations for smoothing of several stochastic dynamical processes, including a benchmark Lorenz system. Experimental results show that the DNS is significantly better than a deep Kalman smoother (DKS) and an iterative data-driven nonlinear state estimation (iDANSE) smoother.

Nir Shlezinger, Guy Revach, Anubhab Ghosh et al.

The Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple state-space (SS) models, which may be crude and inaccurate descriptions of the underlying dynamics. Emerging data-centric artificial intelligence (AI) techniques tackle these tasks using deep neural networks (DNNs), which are model-agnostic. Recent developments illustrate the possibility of fusing DNNs with classic Kalman-type filtering, obtaining systems that learn to track in partially known dynamics. This article provides a tutorial-style overview of design approaches for incorporating AI in aiding KF-type algorithms. We review both generic and dedicated DNN architectures suitable for state estimation, and provide a systematic presentation of techniques for fusing AI tools with KFs and for leveraging partial SS modeling and data, categorizing design approaches into task-oriented and SS model-oriented. The usefulness of each approach in preserving the individual strengths of model-based KFs and data-driven DNNs is investigated in a qualitative and quantitative study, whose code is publicly available, illustrating the gains of hybrid model-based/data-driven designs. We also discuss existing challenges and future research directions that arise from fusing AI and Kalman-type algorithms.

Ajay Nayak, Anubhab Ghosh, Arkaprava Basu

Data races in GPU programs pose a threat to the reliability of GPU-accelerated software stacks. Prior works proposed various dynamic (runtime) and static (compile-time) techniques to detect races in GPU programs. However, dynamic techniques often miss critical races, as they require the races to manifest during testing. While static ones can catch such races, they often generate numerous false alarms by conservatively assuming values of variables/parameters that cannot ever occur during any execution of the program. We make a key observation that the host (CPU) code that launches GPU kernels contains crucial semantic information about the values that the GPU kernel's parameters can take during execution. Harnessing this hitherto overlooked information helps accurately detect data races in GPU kernel code. We create HGRD, a new state-of-the-art static analysis technique that performs a holistic analysis of both CPU and GPU code to accurately detect a broad set of true races while minimizing false alarms. While SOTA dynamic techniques, such as iGUARD, miss many true races, HGRD misses none. On the other hand, static techniques such as GPUVerify and FaialAA raise tens of false alarms, where HGRD raises none.

Anubhab Ghosh, Antoine Honoré, Dong Liu et al.

In pursuit of explainability, we develop generative models for sequential data. The proposed models provide state-of-the-art classification results and robust performance for speech phone classification. We combine modern neural networks (normalizing flows) and traditional generative models (hidden Markov models - HMMs). Normalizing flow-based mixture models (NMMs) are used to model the conditional probability distribution given the hidden state in the HMMs. Model parameters are learned through judicious combinations of time-tested Bayesian learning methods and contemporary neural network learning methods. We mainly combine expectation-maximization (EM) and mini-batch gradient descent. The proposed generative models can compute likelihood of a data and hence directly suitable for maximum-likelihood (ML) classification approach. Due to structural flexibility of HMMs, we can use different normalizing flow models. This leads to different types of HMMs providing diversity in data modeling capacity. The diversity provides an opportunity for easy decision fusion from different models. For a standard speech phone classification setup involving 39 phones (classes) and the TIMIT dataset, we show that the use of standard features called mel-frequency-cepstral-coeffcients (MFCCs), the proposed generative models, and the decision fusion together can achieve $86.6\%$ accuracy by generative training only. This result is close to state-of-the-art results, for examples, $86.2\%$ accuracy of PyTorch-Kaldi toolkit [1], and $85.1\%$ accuracy using light gated recurrent units [2]. We do not use any discriminative learning approach and related sophisticated features in this article.

Anubhab Ghosh, Antoine Honoré, Dong Liu et al.

We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM) and the neural network based probability distributions for the hidden states of the HMM, can provide a robust classification performance. The combined model is called normalizing-flow mixture model based HMM (NMM-HMM). It can be trained using a combination of expectation-maximization (EM) and backpropagation. We verify the improved robustness of NMM-HMM classifiers in an application to speech recognition.