In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Rips complex (DR). Assigning the Vietoris-Rips weights to simplices, DR experiences speed-up in the persistence calculations by only considering simplices that appear in the Delaunay triangulation of the point cloud. We document and compare a Python implementation of DR with other simplicial complex constructions for generating persistence diagrams. By imposing sufficient conditions on point cloud data, we are able to theoretically justify the stability of the persistence diagrams produced using DR. When the Delaunay triangulation of the point cloud changes under perturbations of the points, we prove that DR-produced persistence diagrams exhibit instability. Since we cannot guarantee that real-world data will satisfy our stability conditions, we demonstrate the practical robustness of DR for persistent homology in comparison with other simplicial complexes in machine learning applications. We find in our experiments that using DR for an ML-TDA pipeline performs comparatively well as using other simplicial complex constructions.

The extent to which advanced waveform analysis of non-invasive physiological signals can diagnose levels of hypovolemia remains insufficiently explored. The present study explores the discriminative ability of a deep learning (DL) framework to classify levels of ongoing hypovolemia, simulated via novel dynamic lower body negative pressure (LBNP) model among healthy volunteers. We used a dynamic LBNP protocol as opposed to the traditional model, where LBNP is applied in a predictable step-wise, progressively descending manner. This dynamic LBNP version assists in circumventing the problem posed in terms of time dependency, as in real-life pre-hospital settings, intravascular blood volume may fluctuate due to volume resuscitation. A supervised DL-based framework for ternary classification was realized by segmenting the underlying noninvasive signal and labeling segments with corresponding LBNP target levels. The proposed DL model with two inputs was trained with respective time-frequency representations extracted on waveform segments to classify each of them into blood volume loss: Class 1 (mild); Class 2 (moderate); or Class 3 (severe). At the outset, the latent space derived at the end of the DL model via late fusion among both inputs assists in enhanced classification performance. When evaluated in a 3-fold cross-validation setup with stratified subjects, the experimental findings demonstrated PPG to be a potential surrogate for variations in blood volume with average classification performance, AUROC: 0.8861, AUPRC: 0.8141, $F1$-score:72.16%, Sensitivity:79.06 %, and Specificity:89.21 %. Our proposed DL algorithm on PPG signal demonstrates the possibility of capturing the complex interplay in physiological responses related to both bleeding and fluid resuscitation using this challenging LBNP setup.

Do bilingual Russian-French authors of the end of the twentieth century such as Andre\"i Makine, Val\'ery Afanassiev, Vladimir F\'edorovski, Iegor Gran, Luba Jurgenson have common stylistic traits in the novels they wrote in French? Can we distinguish between them and non-bilingual French writers' texts? Is the phenomenon of interference observable in French texts of Russian authors? This paper applies authorship attribution methods including Support Vector Machine (SVM), $K$-Nearest Neighbors (KNN), Ridge classification, and Neural Network to answer these questions.

This work profoundly analyzes discrete self-supervised speech representations (units) through the eyes of Generative Spoken Language Modeling (GSLM). Following the findings of such an analysis, we propose practical improvements to the discrete unit for the GSLM. First, we start comprehending these units by analyzing them in three axes: interpretation, visualization, and resynthesis. Our analysis finds a high correlation between the speech units to phonemes and phoneme families, while their correlation with speaker or gender is weaker. Additionally, we found redundancies in the extracted units and claim that one reason may be the units' context. Following this analysis, we propose a new, unsupervised metric to measure unit redundancies. Finally, we use this metric to develop new methods that improve the robustness of units' clustering and show significant improvement considering zero-resource speech metrics such as ABX. Code and analysis tools are available under the following link: https://github.com/slp-rl/SLM-Discrete-Representations

Federated Learning (FL) is a novel distributed machine learning approach to leverage data from Internet of Things (IoT) devices while maintaining data privacy. However, the current FL algorithms face the challenges of non-independent and identically distributed (non-IID) data, which causes high communication costs and model accuracy declines. To address the statistical imbalances in FL, we propose a clustered data sharing framework which spares the partial data from cluster heads to credible associates through device-to-device (D2D) communication. Moreover, aiming at diluting the data skew on nodes, we formulate the joint clustering and data sharing problem based on the privacy-preserving constrained graph. To tackle the serious coupling of decisions on the graph, we devise a distribution-based adaptive clustering algorithm (DACA) basing on three deductive cluster-forming conditions, which ensures the maximum yield of data sharing. The experiments show that the proposed framework facilitates FL on non-IID datasets with better convergence and model accuracy under a limited communication environment.

We introduce two new classes of exact Markov chain Monte Carlo (MCMC) samplers for inference in latent dynamical models. The first one, which we coin auxiliary Kalman samplers, relies on finding a linear Gaussian state-space model approximation around the running trajectory corresponding to the state of the Markov chain. The second, that we name auxiliary particle Gibbs samplers corresponds to deriving good local proposals in an auxiliary Feynman--Kac model for use in particle Gibbs. Both samplers are controlled by augmenting the target distribution with auxiliary observations, resulting in an efficient Gibbs sampling routine. We discuss the relative statistical and computational performance of the samplers introduced, and show how to parallelise the auxiliary samplers along the time dimension. We illustrate the respective benefits and drawbacks of the resulting algorithms on classical examples from the particle filtering literature.

In stochastic optimization, a common tool to deal sequentially with large sample is to consider the well-known stochastic gradient algorithm. Nevertheless, since the stepsequence is the same for each direction, this can lead to bad results in practice in case of ill-conditionned problem. To overcome this, adaptive gradient algorithms such that Adagrad or Stochastic Newton algorithms should be prefered. This paper is devoted to the non asymptotic analyis of these adaptive gradient algorithms for strongly convex objective. All the theoretical results will be adapted to linear regression and regularized generalized linear model for both Adagrad and Stochastic Newton algorithms.

The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the spike probability is stochastically increasing and constructed from the stick-breaking representation of a Dirichlet process prior. As a first contribution, this CUSP prior is extended by involving arbitrary stick-breaking representations arising from beta distributions. As a second contribution, we prove that exchangeable spike-and-slab priors, which are popular and widely used in sparse Bayesian factor analysis, can be represented as a finite generalized CUSP prior, which is easily obtained from the decreasing order statistics of the slab probabilities. Hence, exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index in the loading matrix increases, without imposing explicit order constraints on the slab probabilities. An application to sparse Bayesian factor analysis illustrates the usefulness of the findings of this paper. A new exchangeable spike-and-slab shrinkage prior based on the triple gamma prior of Cadonna et al. (2020) is introduced and shown to be helpful for estimating the unknown number of factors in a simulation study.

Clustering is commonly performed as an initial analysis step for uncovering structure in 'omics datasets, e.g. to discover molecular subtypes of disease. The high-throughput, high-dimensional nature of these datasets means that they provide information on a diverse array of different biomolecular processes and pathways. Different groups of variables (e.g. genes or proteins) will be implicated in different biomolecular processes, and hence undertaking analyses that are limited to identifying just a single clustering partition of the whole dataset is therefore liable to conflate the multiple clustering structures that may arise from these distinct processes. To address this, we propose a multi-view Bayesian mixture model that identifies groups of variables (``views"), each of which defines a distinct clustering structure. We consider applications in stratified medicine, for which our principal goal is to identify clusters of patients that define distinct, clinically actionable disease subtypes. We adopt the semi-supervised, outcome-guided mixture modelling approach of Bayesian profile regression that makes use of a response variable in order to guide inference toward the clusterings that are most relevant in a stratified medicine context. We present the model, together with illustrative simulation examples, and examples from pan-cancer proteomics. We demonstrate how the approach can be used to perform integrative clustering, and consider an example in which different 'omics datasets are integrated in the context of breast cancer subtyping.

Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise typically required for the process to succeed can often hinder the adoption of ITPs. A recent strain of work has investigated methods to incorporate machine learning models trained on ITP user activity traces as a viable path towards full automation. While a valuable line of investigation, many problems still require human supervision to be completed fully, thus applying learning methods to assist the user with useful recommendations can prove more fruitful. Following the vein of user assistance, we introduce CoProver, a proof recommender system based on transformers, capable of learning from past actions during proof construction, all while exploring knowledge stored in the ITP concerning previous proofs. CoProver employs a neurally learnt sequence-based encoding of sequents, capturing long distance relationships between terms and hidden cues therein. We couple CoProver with the Prototype Verification System (PVS) and evaluate its performance on two key areas, namely: (1) Next Proof Action Recommendation, and (2) Relevant Lemma Retrieval given a library of theories. We evaluate CoProver on a series of well-established metrics originating from the recommender system and information retrieval communities, respectively. We show that CoProver successfully outperforms prior state of the art applied to recommendation in the domain. We conclude by discussing future directions viable for CoProver (and similar approaches) such as argument prediction, proof summarization, and more.