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 (noisy) 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.

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. 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.

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.

We propose DANSE - a data-driven non-linear state estimation method. DANSE provides a closed-form posterior of the state of a model-free process, given linear measurements of the state in a Bayesian setup, like the celebrated Kalman filter (KF). Non-linear dynamics of the state are captured by data-driven recurrent neural networks (RNNs). The training of DANSE combines maximum-likelihood and gradient-descent in an unsupervised framework, i.e. only measurement data and no process data are required. Using simulated linear and non-linear process models, we demonstrate that DANSE - without knowledge of the process model - provides competitive performance against model-based approaches such as KF, unscented KF (UKF), extended KF (EKF), and a hybrid approach such as KalmanNet.

The Sun's activity, which is associated with the solar magnetic cycle, creates a dynamic environment in space known as space weather. Severe space weather can disrupt space-based and Earth-based technologies. Slow decadal-scale variations on solar-cycle timescales are important for radiative forcing of the Earth's atmosphere and impact satellite lifetimes and atmospheric dynamics. Predicting the solar magnetic cycle is therefore of critical importance for humanity. In this context, a novel development is the application of machine-learning algorithms for solar-cycle forecasting. Diverse approaches have been developed for this purpose; however, with no consensus across different techniques and physics-based approaches. Here, we first explore the performance of four different machine-learning algorithms - all of them belonging to a class called Recurrent Neural Networks (RNNs) - in predicting simulated sunspot cycles based on a widely studied, stochastically forced, nonlinear time-delay solar dynamo model. We conclude that the algorithm Echo State Network (ESN) performs the best, but predictability is limited to only one future sunspot cycle, in agreement with recent physical insights. Subsequently, we train the ESN algorithm and a modified version of it (MESN) with solar-cycle observations to forecast Cycles 22 - 25. We obtain accurate hindcasts for Solar Cycles 22 - 24. For Solar Cycle 25 the ESN algorithm forecasts a peak amplitude of 131 +/- 14 sunspots around July 2024 and indicates a cycle length of approximately 10 years. The MESN forecasts a peak of 137 +/- 2 sunspots around April 2024, with the same cycle length. Qualitatively, both forecasts indicate that Cycle 25 will be slightly stronger than Cycle 24 but weaker than Cycle 23. Our novel approach bridges physical model-based forecasts with machine-learning-based approaches, achieving consistency across these diverse techniques.

We develop a time-varying normalizing flow (TVNF) for explicit generative modeling of dynamical signals. Being explicit, it can generate samples of dynamical signals, and compute the likelihood of a (given) dynamical signal sample. In the proposed model, signal flow in the layers of the normalizing flow is a function of time, which is realized using an encoded representation that is the output of a recurrent neural network (RNN). Given a set of dynamical signals, the parameters of TVNF are learned according to maximum-likelihood approach in conjunction with gradient descent (backpropagation). Use of the proposed model is illustrated for a toy application scenario - maximum-likelihood based speech-phone classification task.

The task of Phone recognition is a fundamental task in Speech recognition and often serves a critical role in bench-marking purposes. Researchers have used a variety of models used in the past to address this task, using both generative and discriminative learning approaches. Among them, generative approaches such as the use of Gaussian mixture model-based hidden Markov models are always favored because of their mathematical tractability. However, the use of generative models such as hidden Markov models and its hybrid varieties is no longer in fashion owing to a large inclination to discriminative learning approaches, which have been found to perform better. The only downside is that these approaches do not always ensure mathematical tractability or convergence guarantees as opposed to their generative counterparts. So, the research problem was to investigate whether there could be a process of augmenting the modeling capability of generative Models using a kind of neural network based architectures that could simultaneously prove mathematically tractable and expressive. Normalizing flows are a class of generative models that have been garnered a lot of attention recently in the field of density estimation and offer a method for exact likelihood computation and inference. In this project, a few varieties of Normalizing flow-based hidden Markov models were used for the task of Phone recognition on the TIMIT dataset. It was been found that these models and their mixture model varieties outperformed classical generative model varieties like Gaussian mixture models. A decision fusion approach using classical Gaussian and Normalizing flow-based mixtures showed competitive results compared to discriminative learning approaches. Further analysis based on classes of speech phones was carried out to compare the generative models used. Additionally, a study of the robustness of these algorithms to noisy speech conditions was also carried out.

Uppgiften för fonemigenkänning är en grundläggande uppgift i taligenkänning och tjänar ofta en kritisk roll i benchmarkingändamål. Forskare har använt en mängd olika modeller som använts tidigare för att hantera denna uppgift genom att använda både generativa och diskriminerande inlärningssätt. Bland dem är generativa tillvägagångssätt som användning av Gaussian-blandnings modellbaserade dolda Markov-modeller alltid föredragna på grund av deras matematiska spårbarhet. Men användningen av generativa modeller som dolda Markov-modeller och dess hybridvarianter är inte längre på mode på grund av en stor lutning till diskriminerande inlärningsmetoder, som har visat sig fungera bättre. Den enda nackdelen är att dessa tillvägagångssätt inte alltid säkerställer matematisk spårbarhet eller konvergensgarantier i motsats till deras generativa motsvarigheter. Således var forskningsproblemet att undersöka om det kan finnas en process för att förstärka modelleringsförmågan hos generativa modeller med hjälp av ett slags neurala nätverksbaserade arkitekturer som samtidigt kunde visa sig matematiskt spårbart och uttrycksfullt. Normaliseringsflöden är en klass generativa modeller som nyligen har fått mycket uppmärksamhet inom området för densitetsberäkning och erbjuder en metod för exakt sannolikhetsberäkning och slutsats. I detta projekt användes några få varianter av Normaliserande flödesbaserade dolda Markov-modeller för uppgiften att fonemigenkänna i TIMIT-datasatsen. Det visade sig att dessa modeller och deras blandningsmodellvarianter överträffade klassiska generativa modellvarianter som Gaussiska blandningsmodeller. Ett beslutssmältningsstrategi med klassiska Gaussiska och Normaliserande flödesbaserade blandningar visade konkurrenskraftiga resultat jämfört med diskriminerande inlärningsmetoder. Ytterligare analys baserat på klasser av talsignaler utfördes för att jämföra de generativa modellerna som användes. Dessutom genomfördes en studie av robustheten hos dessa algoritmer till bullriga talförhållanden.

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.