The number of modes in a probability density function is representative of the model's complexity and can also be viewed as the number of existing subpopulations. Despite its relevance, little research has been devoted to its estimation. Focusing on the univariate setting, we propose a novel approach targeting prediction accuracy inspired by some overlooked aspects of the problem. We argue for the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view blending global and local density properties. Our method builds upon a combination of flexible kernel estimators and parsimonious compositional splines. Feature exploration, model selection and mode testing are implemented in the Bayesian inference paradigm, providing soft solutions and allowing to incorporate expert judgement in the process. The usefulness of our proposal is illustrated through a case study in sports analytics, showcasing multiple companion visualisation tools. A thorough simulation study demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, our method emerges as a top-tier alternative offering innovative solutions for analysts.

We present NusaCrowd, a collaborative initiative to collect and unify existing resources for Indonesian languages, including opening access to previously non-public resources. Through this initiative, we have brought together 137 datasets and 118 standardized data loaders. The quality of the datasets has been assessed manually and automatically, and their value is demonstrated through multiple experiments. NusaCrowd's data collection enables the creation of the first zero-shot benchmarks for natural language understanding and generation in Indonesian and the local languages of Indonesia. Furthermore, NusaCrowd brings the creation of the first multilingual automatic speech recognition benchmark in Indonesian and the local languages of Indonesia. Our work strives to advance natural language processing (NLP) research for languages that are under-represented despite being widely spoken.

In high dimensional variable selection problems, statisticians often seek to design multiple testing procedures that control the False Discovery Rate (FDR), while concurrently identifying a greater number of relevant variables. Model-X methods, such as Knockoffs and conditional randomization tests, achieve the primary goal of finite-sample FDR control, assuming a known distribution of covariates. However, whether these methods can also achieve the secondary goal of maximizing discoveries remains uncertain. In fact, designing procedures to discover more relevant variables with finite-sample FDR control is a largely open question, even within the arguably simplest linear models. In this paper, we develop near-optimal multiple testing procedures for high dimensional Bayesian linear models with isotropic covariates. We introduce Model-X procedures that provably control the frequentist FDR from finite samples, even when the model is misspecified, and conjecturally achieve near-optimal power when the data follow the Bayesian linear model. Our proposed procedure, PoEdCe, incorporates three key ingredients: Posterior Expectation, distilled Conditional randomization test (dCRT), and the Benjamini-Hochberg procedure with e-values (eBH). The optimality conjecture of PoEdCe is based on a heuristic calculation of its asymptotic true positive proportion (TPP) and false discovery proportion (FDP), which is supported by methods from statistical physics as well as extensive numerical simulations. Our result establishes the Bayesian linear model as a benchmark for comparing the power of various multiple testing procedures.

The use of Machine Learning (ML) has rapidly spread across several fields, having encountered many applications in Structural Dynamics and Vibroacoustic (SD\&V). The increasing capabilities of ML to unveil insights from data, driven by unprecedented data availability, algorithms advances and computational power, enhance decision making, uncertainty handling, patterns recognition and real-time assessments. Three main applications in SD\&V have taken advantage of these benefits. In Structural Health Monitoring, ML detection and prognosis lead to safe operation and optimized maintenance schedules. System identification and control design are leveraged by ML techniques in Active Noise Control and Active Vibration Control. Finally, the so-called ML-based surrogate models provide fast alternatives to costly simulations, enabling robust and optimized product design. Despite the many works in the area, they have not been reviewed and analyzed. Therefore, to keep track and understand this ongoing integration of fields, this paper presents a survey of ML applications in SD\&V analyses, shedding light on the current state of implementation and emerging opportunities. The main methodologies, advantages, limitations, and recommendations based on scientific knowledge were identified for each of the three applications. Moreover, the paper considers the role of Digital Twins and Physics Guided ML to overcome current challenges and power future research progress. As a result, the survey provides a broad overview of the present landscape of ML applied in SD\&V and guides the reader to an advanced understanding of progress and prospects in the field.

Due to complexity and dynamics of construction work, resource, and cash flows, poor management of them usually leads to time and cost overruns, bankruptcy, even project failure. Existing approaches in construction failed to achieve optimal control of resource flow in a dynamic environment with uncertainty. Therefore, this paper introducess a model and method to adaptive control the resource flows to optimize the work and cash flows of construction projects. First, a mathematical model based on a partially observable Markov decision process is established to formulate the complex interactions of construction work, resource, and cash flows as well as uncertainty and variability of diverse influence factors. Meanwhile, to efficiently find the optimal solutions, a deep reinforcement learning (DRL) based method is introduced to realize the continuous adaptive optimal control of labor and material flows, thereby optimizing the work and cash flows. To assist the training process of DRL, a simulator based on discrete event simulation is also developed to mimic the dynamic features and external environments of a project. Experiments in simulated scenarios illustrate that our method outperforms the vanilla empirical method and genetic algorithm, possesses remarkable capability in diverse projects and external environments, and a hybrid agent of DRL and empirical method leads to the best result. This paper contributes to adaptive control and optimization of coupled work, resource, and cash flows, and may serve as a step stone for adopting DRL technology in construction project management.

Differential privacy is the state-of-the-art definition for privacy, guaranteeing that any analysis performed on a sensitive dataset leaks no information about the individuals whose data are contained therein. In this thesis, we develop differentially private algorithms to analyze distributed and streaming data. In the distributed model, we consider the particular problem of learning -- in a distributed fashion -- a global model of the data, that can subsequently be used for arbitrary analyses. We build upon PrivBayes, a differentially private method that approximates the high-dimensional distribution of a centralized dataset as a product of low-order distributions, utilizing a Bayesian Network model. We examine three novel approaches to learning a global Bayesian Network from distributed data, while offering the differential privacy guarantee to all local datasets. Our work includes a detailed theoretical analysis of the distributed, differentially private entropy estimator which we use in one of our algorithms, as well as a detailed experimental evaluation, using both synthetic and real-world data. In the streaming model, we focus on the problem of estimating the density of a stream of users, which expresses the fraction of all users that actually appear in the stream. We offer one of the strongest privacy guarantees for the streaming model, user-level pan-privacy, which ensures that the privacy of any user is protected, even against an adversary that observes the internal state of the algorithm. We provide a detailed analysis of an existing, sampling-based algorithm for the problem and propose two novel modifications that significantly improve it, both theoretically and experimentally, by optimally using all the allocated "privacy budget."

Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators.

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called "warmup" to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells.

Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing methods mostly assume noisy labels in different pixels are \textit{i.i.d}. However, segmentation label noise usually has strong spatial correlation and has prominent bias in distribution. In this paper, we propose a novel Markov model for segmentation noisy annotations that encodes both spatial correlation and bias. Further, to mitigate such label noise, we propose a label correction method to recover true label progressively. We provide theoretical guarantees of the correctness of the proposed method. Experiments show that our approach outperforms current state-of-the-art methods on both synthetic and real-world noisy annotations.

This paper presents a substantial extension of our work published at ICLR. Our ICLR work advocated for enhancing transferability in adversarial examples by incorporating a Bayesian formulation into model parameters, which effectively emulates the ensemble of infinitely many deep neural networks, while, in this paper, we introduce a novel extension by incorporating the Bayesian formulation into the model input as well, enabling the joint diversification of both the model input and model parameters. Our empirical findings demonstrate that: 1) the combination of Bayesian formulations for both the model input and model parameters yields significant improvements in transferability; 2) by introducing advanced approximations of the posterior distribution over the model input, adversarial transferability achieves further enhancement, surpassing all state-of-the-arts when attacking without model fine-tuning. Moreover, we propose a principled approach to fine-tune model parameters in such an extended Bayesian formulation. The derived optimization objective inherently encourages flat minima in the parameter space and input space. Extensive experiments demonstrate that our method achieves a new state-of-the-art on transfer-based attacks, improving the average success rate on ImageNet and CIFAR-10 by 19.14% and 2.08%, respectively, when comparing with our ICLR basic Bayesian method. We will make our code publicly available.