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We make two contributions to the Isolation Forest method for anomaly and outlier detection. The first contribution is an information-theoretically motivated generalisation of the score function that is used to aggregate the scores across random tree estimators. This generalisation allows one to take into account not just the ensemble average across trees but instead the whole distribution. The second contribution is an alternative scoring function at the level of the individual tree estimator, in which we replace the depth-based scoring of the Isolation Forest with one based on hyper-volumes associated to an isolation tree's leaf nodes. We motivate the use of both of these methods on generated data and also evaluate them on 34 datasets from the recent and exhaustive ``ADBench'' benchmark, finding significant improvement over the standard isolation forest for both variants on some datasets and improvement on average across all datasets for one of the two variants. The code to reproduce our results is made available as part of the submission.

Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows for discontinuities penalizing their number by a linear term. The corresponding estimates are cubic smoothing splines with discontinuities (CSSD) which serve as representations of piecewise smooth signals and facilitate exploratory data analysis. However, computing the estimates requires solving a non-convex optimization problem. So far, efficient and exact solvers exist only for a discrete approximation based on equidistantly sampled data. In this work, we propose an efficient solver for the continuous minimization problem with non-equidistantly sampled data. Its worst case complexity is quadratic in the number of data points, and if the number of detected discontinuities scales linearly with the signal length, we observe linear growth in runtime. This efficient algorithm allows to use cross validation for automatic selection of the hyperparameters within a reasonable time frame on standard hardware. We provide a reference implementation and supplementary material. We demonstrate the applicability of the approach for the aforementioned tasks using both simulated and real data.

In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with typicality are considered under a (many-valued) ``concept-wise" multipreference semantics. The semantics is used to provide a preferential interpretation of MultiLayer Perceptrons (MLPs). A model checking and an entailment based approach are exploited in the verification of conditional properties of MLPs.

In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an inadequate resolution might introduce numerical noise that triggers premature transition. With AMR, we enable the design of three different and independent meshes for the non-linear base flow, the linear direct and adjoint solutions. Each of those is designed to reduce the truncation and quadrature errors for its respective solution, which are measured via the spectral error indicator. We provide details about the workflow and the refining procedure. The numerical framework is validated for the two-dimensional flow past a circular cylinder, computing a portion of the spectrum for the linearised direct and adjoint Navier-Stokes operators.

In this paper, the joint distribution of the sum and maximum of independent, not necessarily identically distributed, nonnegative random variables is studied for two cases: i) continuous and ii) discrete random variables. First, a recursive formula of the joint cumulative distribution function (CDF) is derived in both cases. Then, recurrence relations of the joint probability density function (PDF) and the joint probability mass function (PMF) are given in the former and the latter case, respectively. Interestingly, there is a fundamental difference between the joint PDF and PMF. The proofs are simple and mainly based on the following tools from calculus and discrete mathematics: differentiation under the integral sign (also known as Leibniz's integral rule), the law of total probability, and mathematical induction. Finally, this work generalizes previous results in the literature.

In this paper, we evaluate the portability of the SYCL programming model on some of the latest CPUs and GPUs from a wide range of vendors, utilizing the two main compilers: DPC++ and hipSYCL/OpenSYCL. Both compilers currently support GPUs from all three major vendors; we evaluate performance on the Intel(R) Data Center GPU Max 1100, the NVIDIA A100 GPU, and the AMD MI250X GPU. Support on CPUs currently is less established, with DPC++ only supporting x86 CPUs through OpenCL, however, OpenSYCL does have an OpenMP backend capable of targeting all modern CPUs; we benchmark the Intel Xeon Platinum 8360Y Processor (Ice Lake), the AMD EPYC 9V33X (Genoa-X), and the Ampere Altra platforms. We study a range of primarily bandwidth-bound applications implemented using the OPS and OP2 DSLs, evaluate different formulations in SYCL, and contrast their performance to "native" programming approaches where available (CUDA/HIP/OpenMP). On GPU architectures SCYL on average even slightly outperforms native approaches, while on CPUs it falls behind - highlighting a continued need for improving CPU performance. While SYCL does not solve all the challenges of performance portability (e.g. needing different algorithms on different hardware), it does provide a single programming model and ecosystem to target most current HPC architectures productively.

In this paper, we present a method that allows to further improve speech enhancement obtained with recently introduced Deep Neural Network (DNN) models. We propose a multi-channel refinement method of time-frequency masks obtained with single-channel DNNs, which consists of an iterative Complex Gaussian Mixture Model (CGMM) based algorithm, followed by optimum spatial filtration. We validate our approach on time-frequency masks estimated with three recent deep learning models, namely DCUnet, DCCRN, and FullSubNet. We show that our method with the proposed mask refinement procedure allows to improve the accuracy of estimated masks, in terms of the Area Under the ROC Curve (AUC) measure, and as a consequence the overall speech quality of the enhanced speech signal, as measured by PESQ improvement, and that the improvement is consistent across all three DNN models.

In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain a new Filon-Clenshaw-Curtis-Smolyak (FCCS) rule for oscillatory integrals with linear phase over the $d-$dimensional cube $[-1,1]^d$. By combining stability and convergence estimates for the FCC rule with error estimates for the Smolyak interpolation operator, we obtain an error estimate for the FCCS rule, consisting of the product of a Smolyak-type error estimate multiplied by a term that decreases with $\mathcal{O}(k^{-\tilde{d}})$, where $k$ is the wavenumber and $\tilde{d}$ is the number of oscillatory dimensions. If all dimensions are oscillatory, a higher negative power of $k$ appears in the estimate. As an application, we consider the forward problem of uncertainty quantification (UQ) for a one-space-dimensional Helmholtz problem with wavenumber $k$ and a random heterogeneous refractive index, depending in an affine way on $d$ i.i.d. uniform random variables. After applying a classical hybrid numerical-asymptotic approximation, expectations of functionals of the solution of this problem can be formulated as a sum of oscillatory integrals over $[-1,1]^d$, which we compute using the FCCS rule. We give numerical results for the FCCS rule and the UQ algorithm showing that accuracy improves when both $k$ and the order of the rule increase. We also give results for dimension-adaptive sparse grid FCCS quadrature showing its efficiency as dimension increases.

This paper proposes a method for extracting a lightweight subset from a text-to-speech (TTS) corpus ensuring synthetic speech quality. In recent years, methods have been proposed for constructing large-scale TTS corpora by collecting diverse data from massive sources such as audiobooks and YouTube. Although these methods have gained significant attention for enhancing the expressive capabilities of TTS systems, they often prioritize collecting vast amounts of data without considering practical constraints like storage capacity and computation time in training, which limits the available data quantity. Consequently, the need arises to efficiently collect data within these volume constraints. To address this, we propose a method for selecting the core subset~(known as \textit{core-set}) from a TTS corpus on the basis of a \textit{diversity metric}, which measures the degree to which a subset encompasses a wide range. Experimental results demonstrate that our proposed method performs significantly better than the baseline phoneme-balanced data selection across language and corpus size.

The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established and then their probabilistic properties, such as characteristic function, moments, quadratic forms as well as transformation properties, are investigated.