We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the performances of the empirical risk minimisation (ERM) using $\ell_2$-regularised $\ell_2$, $\ell_1$, and Huber losses, which are the standard approach to such problems. We focus on two metrics for the performance: the generalisation error to similar datasets with outliers, and the estimation error of the original, unpolluted function. Our results are compared with the information theoretic Bayes-optimal estimation bound. For the generalization error, we find that optimally-regularised ERM is asymptotically consistent in the large sample complexity limit if one perform a simple calibration, and compute the rates of convergence. For the estimation error however, we show that due to a norm calibration mismatch, the consistency of the estimator requires an oracle estimate of the optimal norm, or the presence of a cross-validation set not corrupted by the outliers. We examine in detail how performance depends on the loss function and on the degree of outlier corruption in the training set and identify a region of parameters where the optimal performance of the Huber loss is identical to that of the $\ell_2$ loss, offering insights into the use cases of different loss functions.

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose asymptotic variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture estimator to compute Bayesian LOO-CV criteria. Our method retains the simplicity and computational convenience of classical approaches, while guaranteeing finite asymptotic variance of the resulting estimators. Both theoretical and numerical results are provided to illustrate the improved robustness and efficiency. The computational benefits are particularly significant in high-dimensional problems, allowing to perform Bayesian LOO-CV for a broader range of models, and datasets with highly influential observations. The proposed methodology is easily implementable in standard probabilistic programming software and has a computational cost roughly equivalent to fitting the original model once.

Microorganisms are found in almost every environment, including the soil, water, air, and inside other organisms, like animals and plants. While some microorganisms cause diseases, most of them help in biological processes such as decomposition, fermentation and nutrient cycling. A lot of research has gone into studying microbial communities in various environments and how their interactions and relationships can provide insights into various diseases. Co-occurrence network inference algorithms help us understand the complex associations of micro-organisms, especially bacteria. Existing network inference algorithms employ techniques such as correlation, regularized linear regression, and conditional dependence, which have different hyper-parameters that determine the sparsity of the network. Previous methods for evaluating the quality of the inferred network include using external data, and network consistency across sub-samples, both which have several drawbacks that limit their applicability in real microbiome composition data sets. We propose a novel cross-validation method to evaluate co-occurrence network inference algorithms, and new methods for applying existing algorithms to predict on test data. Our empirical study shows that the proposed method is useful for hyper-parameter selection (training) and comparing the quality of the inferred networks between different algorithms (testing).

The intensive care unit (ICU) comprises a complex hospital environment, where decisions made by clinicians have a high level of risk for the patients' lives. A comprehensive care pathway must then be followed to reduce p complications. Uncertain, competing and unplanned aspects within this environment increase the difficulty in uniformly implementing the care pathway. Readmission contributes to this pathway's difficulty, occurring when patients are admitted again to the ICU in a short timeframe, resulting in high mortality rates and high resource utilisation. Several works have tried to predict readmission through patients' medical information. Although they have some level of success while predicting readmission, those works do not properly assess, characterise and understand readmission prediction. This work proposes a standardised and explainable machine learning pipeline to model patient readmission on a multicentric database (i.e., the eICU cohort with 166,355 patients, 200,859 admissions and 6,021 readmissions) while validating it on monocentric (i.e., the MIMIC IV cohort with 382,278 patients, 523,740 admissions and 5,984 readmissions) and multicentric settings. Our machine learning pipeline achieved predictive performance in terms of the area of the receiver operating characteristic curve (AUC) up to 0.7 with a Random Forest classification model, yielding an overall good calibration and consistency on validation sets. From explanations provided by the constructed models, we could also derive a set of insightful conclusions, primarily on variables related to vital signs and blood tests (e.g., albumin, blood urea nitrogen and hemoglobin levels), demographics (e.g., age, and admission height and weight), and ICU-associated variables (e.g., unit type). These insights provide an invaluable source of information during clinicians' decision-making while discharging ICU patients.

This PhD thesis is focused on the central idea that single neurons in the brain should be regarded as temporally precise and highly complex spatio-temporal pattern recognizers. This is opposed to the prevalent view of biological neurons as simple and mainly spatial pattern recognizers by most neuroscientists today. In this thesis, I will attempt to demonstrate that this is an important distinction, predominantly because the above-mentioned computational properties of single neurons have far-reaching implications with respect to the various brain circuits that neurons compose, and on how information is encoded by neuronal activity in the brain. Namely, that these particular "low-level" details at the single neuron level have substantial system-wide ramifications. In the introduction we will highlight the main components that comprise a neural microcircuit that can perform useful computations and illustrate the inter-dependence of these components from a system perspective. In chapter 1 we discuss the great complexity of the spatio-temporal input-output relationship of cortical neurons that are the result of morphological structure and biophysical properties of the neuron. In chapter 2 we demonstrate that single neurons can generate temporally precise output patterns in response to specific spatio-temporal input patterns with a very simple biologically plausible learning rule. In chapter 3, we use the differentiable deep network analog of a realistic cortical neuron as a tool to approximate the gradient of the output of the neuron with respect to its input and use this capability in an attempt to teach the neuron to perform nonlinear XOR operation. In chapter 4 we expand chapter 3 to describe extension of our ideas to neuronal networks composed of many realistic biological spiking neurons that represent either small microcircuits or entire brain regions.

Quantum computers can theoretically have significant acceleration over classical computers; but, the near-future era of quantum computing is limited due to small number of qubits that are also error prone. Quilt is a framework for performing multi-class classification task designed to work effectively on current error-prone quantum computers. Quilt is evaluated with real quantum machines as well as with projected noise levels as quantum machines become more noise-free. Quilt demonstrates up to 85% multi-class classification accuracy with the MNIST dataset on a five-qubit system.

Due to the lack of more efficient diagnostic tools for monkeypox, its spread remains unchecked, presenting a formidable challenge to global health. While the high efficacy of deep learning models for monkeypox diagnosis has been demonstrated in related studies, the overlook of inference speed, the parameter size and diagnosis performance for early-stage monkeypox renders the models inapplicable in real-world settings. To address these challenges, we proposed an ultrafast and ultralight network named Fast-MpoxNet. Fast-MpoxNet possesses only 0.27M parameters and can process input images at 68 frames per second (FPS) on the CPU. To counteract the diagnostic performance limitation brought about by the small model capacity, it integrates the attention-based feature fusion module and the multiple auxiliary losses enhancement strategy for better detecting subtle image changes and optimizing weights. Using transfer learning and five-fold cross-validation, Fast-MpoxNet achieves 94.26% Accuracy on the Mpox dataset. Notably, its recall for early-stage monkeypox achieves 93.65%. By adopting data augmentation, our model's Accuracy rises to 98.40% and attains a Practicality Score (A new metric for measuring model practicality in real-time diagnosis application) of 0.80. We also developed an application system named Mpox-AISM V2 for both personal computers and mobile phones. Mpox-AISM V2 features ultrafast responses, offline functionality, and easy deployment, enabling accurate and real-time diagnosis for both the public and individuals in various real-world settings, especially in populous settings during the outbreak. Our work could potentially mitigate future monkeypox outbreak and illuminate a fresh paradigm for developing real-time diagnostic tools in the healthcare field.

The Linguistic Matrix Theory (LMT) programme [1, 2] proposes to use permutation invariant random matrix theories to model the statistical properties of ensembles of matrices arising from machine learning algorithms that learn natural language semantics in the subfields of Computational Linguistics and Natural Language Processing in Artificial 1 Intelligence. The use of vectors to represent word meanings has a well-established history in Computational Linguistics (see for example [3]). This usage was initiated in the field of distributional semantics, the ideas behind which are succinctly captured by J. R. Firth's famous quote "You shall know the meaning of a word by the company it keeps" [38]. Advances in neural network machine learning in Natural Language Processing have led to algorithms that learn meaning vectors from large corpora of text. One such algorithm applied to mining the semantic relation of similarity between words is word2vec [12]. Word2vec has been successfully experimented with in a variety of tasks and datasets (see e.g.

Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the constituent estimators, and least-squares with nonnegativity constraints to learn the combination weights. In this paper, we learn these weights analogously by minimizing an estimate of the population risk subject to a nonnegativity constraint. When the constituent estimators are linear least-squares projections onto nested subspaces separated by at least three dimensions, we show that thanks to a shrinkage effect, the resulting stacked estimator has strictly smaller population risk than best single estimator among them. Here "best" refers to an estimator that minimizes a model selection criterion such as AIC or BIC. In other words, in this setting, the best single estimator is inadmissible. Because the optimization problem can be reformulated as isotonic regression, the stacked estimator requires the same order of computation as the best single estimator, making it an attractive alternative in terms of both performance and implementation.

Employers are adopting algorithmic hiring technology throughout the recruitment pipeline. Algorithmic fairness is especially applicable in this domain due to its high stakes and structural inequalities. Unfortunately, most work in this space provides partial treatment, often constrained by two competing narratives, optimistically focused on replacing biased recruiter decisions or pessimistically pointing to the automation of discrimination. Whether, and more importantly what types of, algorithmic hiring can be less biased and more beneficial to society than low-tech alternatives currently remains unanswered, to the detriment of trustworthiness. This multidisciplinary survey caters to practitioners and researchers with a balanced and integrated coverage of systems, biases, measures, mitigation strategies, datasets, and legal aspects of algorithmic hiring and fairness. Our work supports a contextualized understanding and governance of this technology by highlighting current opportunities and limitations, providing recommendations for future work to ensure shared benefits for all stakeholders.