Applications of the ensemble Kalman filter to high-dimensional problems are feasible only with small ensembles. This necessitates a kind of regularization of the analysis (observation update) problem. We propose a regularization technique based on a new non-stationary, non-parametric spatial model on the sphere. The model termed the Locally Stationary Convolution Model is a constrained version of the general Gaussian process convolution model. The constraints on the location-dependent convolution kernel include local isotropy, positive definiteness as a function of distance, and smoothness as a function of location. The model allows for a rigorous definition of the local spectrum, which is required to be a smooth function of spatial wavenumber. We propose and test an ensemble filter in which prior covariances are postulated to obey the Locally Stationary Convolution Model. The model is estimated online in a two-stage procedure. First, ensemble perturbations are bandpass filtered in several wavenumber bands to extract aggregated local spatial spectra. Second, a neural network recovers the local spectra from sample variances of the filtered fields. In simulation experiments, the new filter was capable of outperforming several existing techniques. With small to moderate ensemble sizes, the improvement was substantial.
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Dysarthria is a motor speech disorder often characterized by reduced speech intelligibility through slow, uncoordinated control of speech production muscles. Automatic Speech recognition (ASR) systems can help dysarthric talkers communicate more effectively. However, robust dysarthria-specific ASR requires a significant amount of training speech, which is not readily available for dysarthric talkers. This paper presents a new dysarthric speech synthesis method for the purpose of ASR training data augmentation. Differences in prosodic and acoustic characteristics of dysarthric spontaneous speech at varying severity levels are important components for dysarthric speech modeling, synthesis, and augmentation. For dysarthric speech synthesis, a modified neural multi-talker TTS is implemented by adding a dysarthria severity level coefficient and a pause insertion model to synthesize dysarthric speech for varying severity levels. To evaluate the effectiveness for synthesis of training data for ASR, dysarthria-specific speech recognition was used. Results show that a DNN-HMM model trained on additional synthetic dysarthric speech achieves WER improvement of 12.2% compared to the baseline, and that the addition of the severity level and pause insertion controls decrease WER by 6.5%, showing the effectiveness of adding these parameters. Overall results on the TORGO database demonstrate that using dysarthric synthetic speech to increase the amount of dysarthric-patterned speech for training has significant impact on the dysarthric ASR systems. In addition, we have conducted a subjective evaluation to evaluate the dysarthric-ness and similarity of synthesized speech. Our subjective evaluation shows that the perceived dysartrhic-ness of synthesized speech is similar to that of true dysarthric speech, especially for higher levels of dysarthria
We propose a dynamic sensor selection approach for deep neural networks (DNNs), which is able to derive an optimal sensor subset selection for each specific input sample instead of a fixed selection for the entire dataset. This dynamic selection is jointly learned with the task model in an end-to-end way, using the Gumbel-Softmax trick to allow the discrete decisions to be learned through standard backpropagation. We then show how we can use this dynamic selection to increase the lifetime of a wireless sensor network (WSN) by imposing constraints on how often each node is allowed to transmit. We further improve performance by including a dynamic spatial filter that makes the task-DNN more robust against the fact that it now needs to be able to handle a multitude of possible node subsets. Finally, we explain how the selection of the optimal channels can be distributed across the different nodes in a WSN. We validate this method on a use case in the context of body-sensor networks, where we use real electroencephalography (EEG) sensor data to emulate an EEG sensor network. We analyze the resulting trade-offs between transmission load and task accuracy.
We propose an end-to-end Automatic Speech Recognition (ASR) system that can be trained on transcribed speech data, text-only data, or a mixture of both. The proposed model uses an integrated auxiliary block for text-based training. This block combines a non-autoregressive multi-speaker text-to-mel-spectrogram generator with a GAN-based enhancer to improve the spectrogram quality. The proposed system can generate a mel-spectrogram dynamically during training. It can be used to adapt the ASR model to a new domain by using text-only data from this domain. We demonstrate that the proposed training method significantly improves ASR accuracy compared to the system trained on transcribed speech only. It also surpasses cascade TTS systems with the vocoder in the adaptation quality and training speed.
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.
Discrete latent space models have recently achieved performance on par with their continuous counterparts in deep variational inference. While they still face various implementation challenges, these models offer the opportunity for a better interpretation of latent spaces, as well as a more direct representation of naturally discrete phenomena. Most recent approaches propose to train separately very high-dimensional prior models on the discrete latent data which is a challenging task on its own. In this paper, we introduce a latent data model where the discrete state is a Markov chain, which allows fast end-to-end training. The performance of our generative model is assessed on a building management dataset and on the publicly available Electricity Transformer Dataset.
Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under very weak assumptions, and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals. To elaborate, our methods take the form of confidence sequences (CS) -- sequences of confidence intervals that are uniformly valid over time. CSs provide valid inference at arbitrary stopping times, incurring no penalties for "peeking" at the data, unlike classical confidence intervals which require the sample size to be fixed in advance. Existing CSs in the literature are nonasymptotic, and hence do not enjoy the aforementioned broad applicability of asymptotic confidence intervals. Our work bridges the gap by giving a definition for "asymptotic CSs", and deriving a universal asymptotic CS that requires only weak CLT-like assumptions. While the CLT approximates the distribution of a sample average by that of a Gaussian at a fixed sample size, we use strong invariance principles (stemming from the seminal 1960s work of Strassen and improvements by Koml\'os, Major, and Tusn\'ady) to uniformly approximate the entire sample average process by an implicit Gaussian process. As an illustration of our theory, we derive asymptotic CSs for the average treatment effect using efficient estimators in observational studies (for which no nonasymptotic bounds can exist even in the fixed-time regime) as well as randomized experiments, enabling causal inference that can be continuously monitored and adaptively stopped.
We study the problem of enumerating Tarski fixed points, focusing on the relational lattices of equivalences, quasiorders and binary relations. We present a polynomial space enumeration algorithm for Tarski fixed points on these lattices and other lattices of polynomial height. It achieves polynomial delay when enumerating fixed points of increasing isotone maps on all three lattices, as well as decreasing isotone maps on the lattice of binary relations. In those cases in which the enumeration algorithm does not guarantee polynomial delay on the three relational lattices on the other hand, we prove exponential lower bounds for deciding the existence of three fixed points when the isotone map is given as an oracle, and that it is NP-hard to find three or more Tarski fixed points. More generally, we show that any deterministic or bounded-error randomized algorithm must perform a number of queries asymptotically at least as large as the lattice width to decide the existence of three fixed points when the isotone map is given as an oracle. Finally, we demonstrate that our findings yield a polynomial delay and space algorithm for listing bisimulations and instances of some related models of behavioral or role equivalence.
We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability estimation. To address the above problem, we employ the general regularization scheme in reproducing kernel Hilbert spaces. The convergence rate of the corresponding regularized algorithm is established by taking into account both the smoothness of the derivative and the capacity of the space in which it is estimated. This is done in terms of general source conditions and the regularized Christoffel functions. We also find that the reconstruction of Radon-Nikodym derivatives at any particular point can be done with high order of accuracy. Our theoretical results are illustrated by numerical simulations.
We study the problem of Online Convex Optimization (OCO) with memory, which allows loss functions to depend on past decisions and thus captures temporal effects of learning problems. In this paper, we introduce dynamic policy regret as the performance measure to design algorithms robust to non-stationary environments, which competes algorithms' decisions with a sequence of changing comparators. We propose a novel algorithm for OCO with memory that provably enjoys an optimal dynamic policy regret in terms of time horizon, non-stationarity measure, and memory length. The key technical challenge is how to control the switching cost, the cumulative movements of player's decisions, which is neatly addressed by a novel switching-cost-aware online ensemble approach equipped with a new meta-base decomposition of dynamic policy regret and a careful design of meta-learner and base-learner that explicitly regularizes the switching cost. The results are further applied to tackle non-stationarity in online non-stochastic control (Agarwal et al., 2019), i.e., controlling a linear dynamical system with adversarial disturbance and convex cost functions. We derive a novel gradient-based controller with dynamic policy regret guarantees, which is the first controller provably competitive to a sequence of changing policies for online non-stochastic control.
Efficient shape-constrained inference for the autocovariance sequence from a reversible Markov chain
In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We examine the theoretical properties of the proposed estimator and provide strong consistency guarantees for our estimator. In particular, for geometrically ergodic reversible Markov chains, we show that our estimator is strongly consistent for the true autocovariance sequence with respect to an $\ell_2$ distance, and that our estimator leads to strongly consistent estimates of the asymptotic variance. Finally, we perform empirical studies to illustrate the theoretical properties of the proposed estimator as well as to demonstrate the effectiveness of our estimator in comparison with other current state-of-the-art methods for Markov chain Monte Carlo variance estimation, including batch means, spectral variance estimators, and the initial convex sequence estimator.
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