The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size, and so a standard approach is subsampling that aims at obtaining the most informative portion of the big data. In the current paper, we explore an existing approach based on leverage scores, proposed for subdata selection in linear model discrimination. Our objective is to propose the aforementioned approach for selecting the most informative data points to estimate unknown parameters in both the first-order linear model and a model with interactions. We conclude that the approach based on leverage scores improves existing approaches, providing simulation experiments as well as a real data application.
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This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.
Advances in next-generation sequencing technology have enabled the high-throughput profiling of metagenomes and accelerated the microbiome study. Recently, there has been a rise in quantitative studies that aim to decipher the microbiome co-occurrence network and its underlying community structure based on metagenomic sequence data. Uncovering the complex microbiome community structure is essential to understanding the role of the microbiome in disease progression and susceptibility. Taxonomic abundance data generated from metagenomic sequencing technologies are high-dimensional and compositional, suffering from uneven sampling depth, over-dispersion, and zero-inflation. These characteristics often challenge the reliability of the current methods for microbiome community detection. To this end, we propose a Bayesian stochastic block model to study the microbiome co-occurrence network based on the recently developed modified centered-log ratio transformation tailored for microbiome data analysis. Our model allows us to incorporate taxonomic tree information using a Markov random field prior. The model parameters are jointly inferred by using Markov chain Monte Carlo sampling techniques. Our simulation study showed that the proposed approach performs better than competing methods even when taxonomic tree information is non-informative. We applied our approach to a real urinary microbiome dataset from postmenopausal women, the first time the urinary microbiome co-occurrence network structure has been studied. In summary, this statistical methodology provides a new tool for facilitating advanced microbiome studies.
The mission of visual brain-computer interfaces (BCIs) is to enhance information transfer rate (ITR) to reach high speed towards real-life communication. Despite notable progress, noninvasive visual BCIs have encountered a plateau in ITRs, leaving it uncertain whether higher ITRs are achievable. In this study, we investigate the information rate limits of the primary visual channel to explore whether we can and how we should build visual BCI with higher information rate. Using information theory, we estimate a maximum achievable ITR of approximately 63 bits per second (bps) with a uniformly-distributed White Noise (WN) stimulus. Based on this discovery, we propose a broadband WN BCI approach that expands the utilization of stimulus bandwidth, in contrast to the current state-of-the-art visual BCI methods based on steady-state visual evoked potentials (SSVEPs). Through experimental validation, our broadband BCI outperforms the SSVEP BCI by an impressive margin of 7 bps, setting a new record of 50 bps. This achievement demonstrates the possibility of decoding 40 classes of noninvasive neural responses within a short duration of only 0.1 seconds. The information-theoretical framework introduced in this study provides valuable insights applicable to all sensory-evoked BCIs, making a significant step towards the development of next-generation human-machine interaction systems.
Within the framework of computational plasticity, recent advances show that the quasi-static response of an elasto-plastic structure under cyclic loadings may exhibit a time multiscale behaviour. In particular, the system response can be computed in terms of time microscale and macroscale modes using a weakly intrusive multi-time Proper Generalized Decomposition (MT-PGD). In this work, such micro-macro characterization of the time response is exploited to build a data-driven model of the elasto-plastic constitutive relation. This can be viewed as a predictor-corrector scheme where the prediction is driven by the macrotime evolution and the correction is performed via a sparse sampling in space. Once the nonlinear term is forecasted, the multi-time PGD algorithm allows the fast computation of the total strain. The algorithm shows considerable gains in terms of computational time, opening new perspectives in the numerical simulation of history-dependent problems defined in very large time intervals.
Early sensory systems in the brain rapidly adapt to fluctuating input statistics, which requires recurrent communication between neurons. Mechanistically, such recurrent communication is often indirect and mediated by local interneurons. In this work, we explore the computational benefits of mediating recurrent communication via interneurons compared with direct recurrent connections. To this end, we consider two mathematically tractable recurrent linear neural networks that statistically whiten their inputs -- one with direct recurrent connections and the other with interneurons that mediate recurrent communication. By analyzing the corresponding continuous synaptic dynamics and numerically simulating the networks, we show that the network with interneurons is more robust to initialization than the network with direct recurrent connections in the sense that the convergence time for the synaptic dynamics in the network with interneurons (resp. direct recurrent connections) scales logarithmically (resp. linearly) with the spectrum of their initialization. Our results suggest that interneurons are computationally useful for rapid adaptation to changing input statistics. Interestingly, the network with interneurons is an overparameterized solution of the whitening objective for the network with direct recurrent connections, so our results can be viewed as a recurrent linear neural network analogue of the implicit acceleration phenomenon observed in overparameterized feedforward linear neural networks.
This paper addresses the benefits of pooling data for shared learning in maintenance operations. We consider a set of systems subject to Poisson degradation that are coupled through an a-priori unknown rate. Decision problems involving these systems are high-dimensional Markov decision processes (MDPs). We present a decomposition result that reduces such an MDP to two-dimensional MDPs, enabling structural analyses and computations. We leverage this decomposition to demonstrate that pooling data can lead to significant cost reductions compared to not pooling.
MultiPA: a multi-task speech pronunciation assessment system for a closed and open response scenario
The design of automatic speech pronunciation assessment can be categorized into closed and open response scenarios, each with strengths and limitations. A system with the ability to function in both scenarios can cater to diverse learning needs and provide a more precise and holistic assessment of pronunciation skills. In this study, we propose a Multi-task Pronunciation Assessment model called MultiPA. MultiPA provides an alternative to Kaldi-based systems in that it has simpler format requirements and better compatibility with other neural network models. Compared with previous open response systems, MultiPA provides a wider range of evaluations, encompassing assessments at both the sentence and word-level. Our experimental results show that MultiPA achieves comparable performance when working in closed response scenarios and maintains more robust performance when directly used for open responses.
Joint models (JM) for longitudinal and survival data have gained increasing interest and found applications in a wide range of clinical and biomedical settings. These models facilitate the understanding of the relationship between outcomes and enable individualized predictions. In many applications, more complex event processes arise, necessitating joint longitudinal and multistate models. However, their practical application can be hindered by computational challenges due to increased model complexity and large sample sizes. Motivated by a longitudinal multimorbidity analysis of large UK health records, we have developed a scalable Bayesian methodology for such joint multistate models that is capable of handling complex event processes and large datasets, with straightforward implementation. We propose two blockwise inference approaches for different inferential purposes based on different levels of decomposition of the multistate processes. These approaches leverage parallel computing, ease the specification of different models for different transitions, and model/variable selection can be performed within a Bayesian framework using Bayesian leave-one-out cross-validation. Using a simulation study, we show that the proposed approaches achieve satisfactory performance regarding posterior point and interval estimation, with notable gains in sampling efficiency compared to the standard estimation strategy. We illustrate our approaches using a large UK electronic health record dataset where we analysed the coevolution of routinely measured systolic blood pressure (SBP) and the progression of multimorbidity, defined as the combinations of three chronic conditions. Our analysis identified distinct association structures between SBP and different disease transitions.
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps into deep learning's abilities to uncover parameters governing intricate behaviors in nonlinear equations. We validate our approach using synthetic data and predefined functions that model system dynamics. By training the neural network with noisy time series data, it fine-tunes the Huber loss function to converge to accurate parameters. We apply our method to damped oscillators, Van der Pol oscillators, Lotka-Volterra systems, and Lorenz systems under multiplicative noise. The trained neural network accurately estimates parameters, evident from closely matching latent dynamics. Comparing true and estimated trajectories visually reinforces our method's precision and robustness. Our study underscores the Huber loss-guided neural network as a versatile tool for parameter estimation, effectively uncovering complex relationships in nonlinear systems. The method navigates noise and uncertainty adeptly, showcasing its adaptability to real-world challenges.
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict new scenarios unobserved before. In this work, we first extend parallel partial Gaussian processes for predicting the vector-valued transition function that links the observations between the current and next time points, and quantify the uncertainty of predictions by posterior sampling. Second, we show the equivalence between the dynamic mode decomposition and the maximum likelihood estimator of the linear mapping matrix in the linear state space model. The connection provides a data generating model of dynamic mode decomposition and thus, uncertainty of predictions can be obtained. Furthermore, we draw close connections between different data-driven models for approximating nonlinear dynamics, through a unified view of data generating models. We study two numerical examples, where the inputs of the dynamics are assumed to be known in the first example and the inputs are unknown in the second example. The examples indicate that uncertainty of forecast can be properly quantified, whereas model or input misspecification can degrade the accuracy of uncertainty quantification.
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