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In this paper, we introduce a causal low-latency low-complexity approach for binaural multichannel blind speaker separation in noisy reverberant conditions. The model, referred to as Group Communication Binaural Filter and Sum Network (GCBFSnet) predicts complex filters for filter-and-sum beamforming in the time-frequency domain. We apply Group Communication (GC), i.e., latent model variables are split into groups and processed with a shared sequence model with the aim of reducing the complexity of a simple model only containing one convolutional and one recurrent module. With GC we are able to reduce the size of the model by up to 83 % and the complexity up to 73 % compared to the model without GC, while mostly retaining performance. Even for the smallest model configuration, GCBFSnet matches the performance of a low-complexity TasNet baseline in most metrics despite the larger size and higher number of required operations of the baseline.

We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A\leq C\leq B$ for standardized $n$-variate functions $A,B$ and discuss the method for constructing this function. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A\leq C\leq B$.

In this paper we explore the concept of sequential inductive prediction intervals using theory from sequential testing. We furthermore introduce a 3-parameter PAC definition of prediction intervals that allows us via simulation to achieve almost sharp bounds with high probability.

In this paper, we propose a new method for the augmentation of numeric and mixed datasets. The method generates additional data points by utilizing cross-validation resampling and latent variable modeling. It is particularly efficient for datasets with moderate to high degrees of collinearity, as it directly utilizes this property for generation. The method is simple, fast, and has very few parameters, which, as shown in the paper, do not require specific tuning. It has been tested on several real datasets; here, we report detailed results for two cases, prediction of protein in minced meat based on near infrared spectra (fully numeric data with high degree of collinearity) and discrimination of patients referred for coronary angiography (mixed data, with both numeric and categorical variables, and moderate collinearity). In both cases, artificial neural networks were employed for developing the regression and the discrimination models. The results show a clear improvement in the performance of the models; thus for the prediction of meat protein, fitting the model to the augmented data resulted in a reduction in the root mean squared error computed for the independent test set by 1.5 to 3 times.

This paper considers the problem of robust iterative Bayesian smoothing in nonlinear state-space models with additive noise using Gaussian approximations. Iterative methods are known to improve smoothed estimates but are not guaranteed to converge, motivating the development of more robust versions of the algorithms. The aim of this article is to present Levenberg-Marquardt (LM) and line-search extensions of the classical iterated extended Kalman smoother (IEKS) as well as the iterated posterior linearisation smoother (IPLS). The IEKS has previously been shown to be equivalent to the Gauss-Newton (GN) method. We derive a similar GN interpretation for the IPLS. Furthermore, we show that an LM extension for both iterative methods can be achieved with a simple modification of the smoothing iterations, enabling algorithms with efficient implementations. Our numerical experiments show the importance of robust methods, in particular for the IEKS-based smoothers. The computationally expensive IPLS-based smoothers are naturally robust but can still benefit from further regularisation.

In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural generalizations of classical information-theoretic divergences, such as the $f$-divergences and the R\'enyi divergence between probability measures, to the context of finite Markov chains. We begin by detailing and deriving fundamental properties of these divergences and notably gives a Markov chain version of the Pinsker's inequality and Chernoff information. We then utilize these notions in a few applications. First, we investigate the binary hypothesis testing problem of Markov chains, where the newly defined R\'enyi divergence between Markov chains and its geometric interpretation play an important role in the analysis. Second, we propose and analyze information-theoretic (Ces\`aro) mixing times and ergodicity coefficients, along with spectral bounds of these notions in the reversible setting. Examples of the random walk on the hypercube, as well as the connections between the critical height of the low-temperature Metropolis-Hastings chain and these proposed ergodicity coefficients, are highlighted.

In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangulations and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014.

We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters; these are then combined to obtain global approximations of the parametric eigenvalues. To gather the non-parametric data, we use non-intrusive contour-integration-based methods, which, however, cannot track eigenvalues that migrate into/out of the contour as the parameter changes. Special strategies are described for performing the combination-over-parameter step despite having only partial information on such migrating eigenvalues. Moreover, we dedicate a special focus to the approximation of eigenvalues that undergo bifurcations. Finally, we propose an adaptive strategy that allows one to effectively apply our method even without any a priori information on the behavior of the sought-after eigenvalues. Numerical tests are performed, showing that our algorithm can achieve remarkably high approximation accuracy.

Sample selection models represent a common methodology for correcting bias induced by data missing not at random. It is well known that these models are not empirically identifiable without exclusion restrictions. In other words, some variables predictive of missingness do not affect the outcome model of interest. The drive to establish this requirement often leads to the inclusion of irrelevant variables in the model. A recent proposal uses adaptive LASSO to circumvent this problem, but its performance depends on the so-called covariance assumption, which can be violated in small to moderate samples. Additionally, there are no tools yet for post-selection inference for this model. To address these challenges, we propose two families of spike-and-slab priors to conduct Bayesian variable selection in sample selection models. These prior structures allow for constructing a Gibbs sampler with tractable conditionals, which is scalable to the dimensions of practical interest. We illustrate the performance of the proposed methodology through a simulation study and present a comparison against adaptive LASSO and stepwise selection. We also provide two applications using publicly available real data. An implementation and code to reproduce the results in this paper can be found at //github.com/adam-iqbal/selection-spike-slab

This paper focuses on the randomized Milstein scheme for approximating solutions to stochastic Volterra integral equations with weakly singular kernels, where the drift coefficients are non-differentiable. An essential component of the error analysis involves the utilization of randomized quadrature rules for stochastic integrals to avoid the Taylor expansion in drift coefficient functions. Finally, we implement the simulation of multiple singular stochastic integral in the numerical experiment by applying the Riemann-Stieltjes integral.