Inference on modern Bayesian Neural Networks (BNNs) often relies on a variational inference treatment, imposing violated assumptions of independence and the form of the posterior. Traditional MCMC approaches avoid these assumptions at the cost of increased computation due to its incompatibility to subsampling of the likelihood. New Piecewise Deterministic Markov Process (PDMP) samplers permit subsampling, though introduce a model specific inhomogenous Poisson Process (IPPs) which is difficult to sample from. This work introduces a new generic and adaptive thinning scheme for sampling from these IPPs, and demonstrates how this approach can accelerate the application of PDMPs for inference in BNNs. Experimentation illustrates how inference with these methods is computationally feasible, can improve predictive accuracy, MCMC mixing performance, and provide informative uncertainty measurements when compared against other approximate inference schemes.

We provide uniform inference and confidence bands for kernel ridge regression (KRR), a widely-used non-parametric regression estimator for general data types including rankings, images, and graphs. Despite the prevalence of these data -- e.g., ranked preference lists in school assignment -- the inferential theory of KRR is not fully known, limiting its role in economics and other scientific domains. We construct sharp, uniform confidence sets for KRR, which shrink at nearly the minimax rate, for general regressors. To conduct inference, we develop an efficient bootstrap procedure that uses symmetrization to cancel bias and limit computational overhead. To justify the procedure, we derive finite-sample, uniform Gaussian and bootstrap couplings for partial sums in a reproducing kernel Hilbert space (RKHS). These imply strong approximation for empirical processes indexed by the RKHS unit ball with logarithmic dependence on the covering number. Simulations verify coverage. We use our procedure to construct a novel test for match effects in school assignment, an important question in education economics with consequences for school choice reforms.

A metric tensor for Riemann manifold Monte Carlo particularly suited for non-linear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log-density gradient covariance (LGC) matrices, which are also proposed and further explored here. The LGCs generalize the Fisher information matrix by measuring the joint information content and dependence structure of both a random variable and the parameters of said variable. Consequently, positive definite Fisher/LGC-based metric tensors may be constructed not only from the observation likelihoods as is current practice, but also from arbitrarily complicated non-linear prior/latent variable structures, provided the LGC may be derived for each conditional distribution used to construct said structures. The proposed methodology is highly automatic and allows for exploitation of any sparsity associated with the model in question. When implemented in conjunction with a Riemann manifold variant of the recently proposed numerical generalized randomized Hamiltonian Monte Carlo processes, the proposed methodology is highly competitive, in particular for the more challenging target distributions associated with Bayesian hierarchical models.

Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The goal of this process is to provide a useful aid to the researcher that will help her/him to identify patterns among the data. Dealing with large databases, such patterns may not be easily detectable without the contribution of a clustering algorithm. This article provides a deep description of the most widely used clustering methodologies accompanied by useful presentations concerning suitable parameter selection and initializations. Simultaneously, this article not only represents a review highlighting the major elements of examined clustering techniques but emphasizes the comparison of these algorithms' clustering efficiency based on 3 datasets, revealing their existing weaknesses and capabilities through accuracy and complexity, during the confrontation of discrete and continuous observations. The produced results help us extract valuable conclusions about the appropriateness of the examined clustering techniques in accordance with the dataset's size.

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modelling assumptions that compromise the real-time capability or accuracy of the subsequent prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modelling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.

We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behaviour, shapes, number of modes, etc., of the resulting weight adjusted empirical distribution. In this article, we substantially enhance the flexibility of such methodology by introducing a nonparametrically imbued distributional constraints on the weights, and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric while allowing for subtle departures. The versatility of the framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task: namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms.

We study the prospects of Gaussian processes (GP), a machine learning (ML) algorithm, as a tool to reconstruct the Hubble parameter $H(z)$ with two upcoming gravitational wave missions, namely the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET). Assuming various background cosmological models, the Hubble parameter has been reconstructed in a non-parametric manner with the help of GP using realistically generated catalogs for each mission. The effects of early-time and late-time priors on the reconstruction of $H(z)$, and hence on the Hubble constant ($H_0$), have also been focused on separately. Our analysis reveals that GP is quite robust in reconstructing the expansion history of the Universe within the observational window of the specific missions under consideration. We further confirm that both eLISA and ET would be able to provide constraints on $H(z)$ and $H_0$ which would be competitive to those inferred from current datasets. In particular, we observe that an eLISA run of $\sim10$-year duration with $\sim80$ detected bright siren events would be able to constrain $H_0$ as good as a $\sim3$-year ET run assuming $\sim 1000$ bright siren event detections. Further improvement in precision is expected for longer eLISA mission durations such as a $\sim15$-year time-frame having $\sim120$ events. Lastly, we discuss the possible role of these future gravitational wave missions in addressing the Hubble tension, for each model, on a case-by-case basis.

The best encoding is the one that is interpretable in nature. In this work, we introduce a novel model that incorporates an interpretable bottleneck-termed the Filter Bank (FB)-at the outset of a Variational Autoencoder (VAE). This arrangement compels the VAE to attend on the most informative segments of the input signal, fostering the learning of a novel encoding ${f_0}$ which boasts enhanced interpretability and clusterability over traditional latent spaces. By deliberately constraining the VAE with this FB, we intentionally constrict its capacity to access broad input domain information, promoting the development of an encoding that is discernible, separable, and of reduced dimensionality. The evolutionary learning trajectory of ${f_0}$ further manifests as a dynamic hierarchical tree, offering profound insights into cluster similarities. Additionally, for handling intricate data configurations, we propose a tailored decoder structure that is symmetrically aligned with FB's architecture. Empirical evaluations highlight the superior efficacy of ISVAE, which compares favorably to state-of-the-art results in clustering metrics across real-world datasets.

Physical human-robot interactions (pHRIs) can improve robot autonomy and reduce physical demands on humans. In this paper, we consider a collaborative task with a considerably long object and no prior knowledge of the object's parameters. An integrated control framework with an online object parameter estimator and a Cartesian object-aware impedance controller is proposed to realize complicated scenarios. During the transportation task, the object parameters are estimated online while a robot and human lift an object. The perturbation motion is incorporated into the null space of the desired trajectory to enhance the estimator accuracy. An object-aware impedance controller is designed using the real-time estimation results to effectively transmit the intended human motion to the robot through the object. Experimental demonstrations of collaborative tasks, including object transportation and assembly tasks, are implemented to show the effectiveness of our proposed method.

k-nearest-neighbor machine translation (kNN-MT) boosts the translation quality of a pre-trained neural machine translation (NMT) model by utilizing translation examples during decoding. Translation examples are stored in a vector database, called a datastore, which contains one entry for each target token from the parallel data it is made from. Due to its size, it is computationally expensive both to construct and to retrieve examples from the datastore. In this paper, we present an efficient and extensible kNN-MT framework, knn-seq, for researchers and developers that is carefully designed to run efficiently, even with a billion-scale large datastore. knn-seq is developed as a plug-in on fairseq and easy to switch models and kNN indexes. Experimental results show that our implemented kNN-MT achieves a comparable gain to the original kNN-MT, and the billion-scale datastore construction took 2.21 hours in the WMT'19 German-to-English translation task. We publish our knn-seq as an MIT-licensed open-source project and the code is available on https://github.com/naist-nlp/knn-seq . The demo video is available on https://youtu.be/zTDzEOq80m0 .