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We present in this paper an informed single-channel dereverberation method based on conditional generation with diffusion models. With knowledge of the room impulse response, the anechoic utterance is generated via reverse diffusion using a measurement consistency criterion coupled with a neural network that represents the clean speech prior. The proposed approach is largely more robust to measurement noise compared to a state-of-the-art informed single-channel dereverberation method, especially for non-stationary noise. Furthermore, we compare to other blind dereverberation methods using diffusion models and show superiority of the proposed approach for large reverberation times. We motivate the presented algorithm by introducing an extension for blind dereverberation allowing joint estimation of the room impulse response and anechoic speech. Audio samples and code can be found online (//uhh.de/inf-sp-derev-dps).

In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we present a strengthened version of Catoni's bound that holds uniformly for all parameter values. This leads to new fast rate and mixed rate bounds that are interpretable and tighter than previous bounds in the literature. Secondly, for losses with more general tail behaviors, we introduce two new parameter-free bounds: a PAC-Bayes Chernoff analogue when the loss' cumulative generating function is bounded, and a bound when the loss' second moment is bounded. These two bounds are obtained using a new technique based on a discretization of the space of possible events for the "in probability" parameter optimization problem. Finally, we extend all previous results to anytime-valid bounds using a simple technique applicable to any existing bound.

Response time has attracted increased interest in educational and psychological assessment for, e.g., measuring test takers' processing speed, improving the measurement accuracy of ability, and understanding aberrant response behavior. Most models for response time analysis are based on a parametric assumption about the response time distribution. The Cox proportional hazard model has been utilized for response time analysis for the advantages of not requiring a distributional assumption of response time and enabling meaningful interpretations with respect to response processes. In this paper, we present a new version of the proportional hazard model, called a latent space accumulator model, for cognitive assessment data based on accumulators for two competing response outcomes, such as correct vs. incorrect responses. The proposed model extends a previous accumulator model by capturing dependencies between respondents and test items across accumulators in the form of distances in a two-dimensional Euclidean space. A fully Bayesian approach is developed to estimate the proposed model. The utilities of the proposed model are illustrated with two real data examples.

Partial differential equations (PDEs) are ubiquitous in science and engineering. Prior quantum algorithms for solving the system of linear algebraic equations obtained from discretizing a PDE have a computational complexity that scales at least linearly with the condition number $\kappa$ of the matrices involved in the computation. For many practical applications, $\kappa$ scales polynomially with the size $N$ of the matrices, rendering a polynomial-in-$N$ complexity for these algorithms. Here we present a quantum algorithm with a complexity that is polylogarithmic in $N$ but is independent of $\kappa$ for a large class of PDEs. Our algorithm generates a quantum state that enables extracting features of the solution. Central to our methodology is using a wavelet basis as an auxiliary system of coordinates in which the condition number of associated matrices is independent of $N$ by a simple diagonal preconditioner. We present numerical simulations showing the effect of the wavelet preconditioner for several differential equations. Our work could provide a practical way to boost the performance of quantum-simulation algorithms where standard methods are used for discretization.

The Plackett--Luce model is a popular approach for ranking data analysis, where a utility vector is employed to determine the probability of each outcome based on Luce's choice axiom. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as the full-, marginal-, and quasi-likelihood. We provide a rank-matching interpretation for the estimating equations of these estimators and analyze their asymptotic behavior as the number of items being compared tends to infinity. In particular, we establish the uniform consistency of these estimators under conditions characterized by the topology of the underlying comparison graph sequence and demonstrate that the proposed conditions are sharp for common sampling scenarios such as the nonuniform random hypergraph model and the hypergraph stochastic block model; we also obtain the asymptotic normality of these estimators and discuss the trade-off between statistical efficiency and computational complexity for practical uncertainty quantification. Both results allow for nonuniform and inhomogeneous comparison graphs with varying edge sizes and different asymptotic orders of edge probabilities. We verify our theoretical findings by conducting detailed numerical experiments.

We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically compatible description of the fluid flow. The scheme is stable for large time steps controlled by the interface transport and is computational efficient due to a linear implicit character. The latter is achieved by linearizing along constant reference states given by the asymptotic analysis of the single-temperature model. Thus, the use of a stiffly accurate IMEX Runge Kutta time integration and the centered treatment of pressure based quantities provably guarantee the asymptotic preserving property of the scheme for weakly compressible Euler equations with variable volume fraction. The properties of the first and second order scheme are validated by several numerical test cases.

This paper describes an efficient unsupervised learning method for a neural source separation model that utilizes a probabilistic generative model of observed multichannel mixtures proposed for blind source separation (BSS). For this purpose, amortized variational inference (AVI) has been used for directly solving the inverse problem of BSS with full-rank spatial covariance analysis (FCA). Although this unsupervised technique called neural FCA is in principle free from the domain mismatch problem, it is computationally demanding due to the full rankness of the spatial model in exchange for robustness against relatively short reverberations. To reduce the model complexity without sacrificing performance, we propose neural FastFCA based on the jointly-diagonalizable yet full-rank spatial model. Our neural separation model introduced for AVI alternately performs neural network blocks and single steps of an efficient iterative algorithm called iterative source steering. This alternating architecture enables the separation model to quickly separate the mixture spectrogram by leveraging both the deep neural network and the multichannel optimization algorithm. The training objective with AVI is derived to maximize the marginalized likelihood of the observed mixtures. The experiment using mixture signals of two to four sound sources shows that neural FastFCA outperforms conventional BSS methods and reduces the computational time to about 2% of that for the neural FCA.

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to tenth order of accuracy. This method requires only one reconstructed value per face for each computational cell. A passage through high-order point values leads to a modest growth of computational cost with increasing discretization order. At a given resolution, these high-order schemes present significantly less numerical dissipation than commonly employed lower-order approaches. Thus, results of comparable accuracy are achievable at a substantially coarser resolution, yielding overall performance gains. We also present a way to include physical dissipative terms: viscosity, magnetic diffusivity and cooling functions, respecting the finite-volume and constrained-transport frameworks.

Two numerical schemes are proposed and investigated for the Yang--Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-valued functions, with similarities to certain formulations of General Relativity. Both schemes are built on the Discrete de Rham (DDR) method, and inherit from its main features: an arbitrary order of accuracy, and applicability to generic polyhedral meshes. They make use of the complex property of the DDR, together with a Lagrange-multiplier approach, to preserve, at the discrete level, a nonlinear constraint associated with the Yang--Mills equations. We also show that the schemes satisfy a discrete energy dissipation (the dissipation coming solely from the implicit time stepping). Issues around the practical implementations of the schemes are discussed; in particular, the assembly of the local contributions in a way that minimises the price we pay in dealing with nonlinear terms, in conjunction with the tensorisation coming from the Lie algebra. Numerical tests are provided using a manufactured solution, and show that both schemes display a convergence in $L^2$-norm of the potential and electrical fields in $\mathcal O(h^{k+1})$ (provided that the time step is of that order), where $k$ is the polynomial degree chosen for the DDR complex. We also numerically demonstrate the preservation of the constraint.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.