We propose a methodology to predict the cardiac epicardial and mediastinal fat volumes in computed tomography images using regression algorithms. The obtained results indicate that it is feasible to predict these fats with a high degree of correlation, thus alleviating the requirement for manual or automatic segmentation of both fat volumes. Instead, segmenting just one of them suffices, while the volume of the other may be predicted fairly precisely. The correlation coefficient obtained by the Rotation Forest algorithm using MLP Regressor for predicting the mediastinal fat based on the epicardial fat was 0.9876, with a relative absolute error of 14.4% and a root relative squared error of 15.7%. The best correlation coefficient obtained in the prediction of the epicardial fat based on the mediastinal was 0.9683 with a relative absolute error of 19.6% and a relative squared error of 24.9%. Moreover, we analysed the feasibility of using linear regressors, which provide an intuitive interpretation of the underlying approximations. In this case, the obtained correlation coefficient was 0.9534 for predicting the mediastinal fat based on the epicardial, with a relative absolute error of 31.6% and a root relative squared error of 30.1%. On the prediction of the epicardial fat based on the mediastinal fat, the correlation coefficient was 0.8531, with a relative absolute error of 50.43% and a root relative squared error of 52.06%. In summary, it is possible to speed up general medical analyses and some segmentation and quantification methods that are currently employed in the state-of-the-art by using this prediction approach, which consequently reduces costs and therefore enables preventive treatments that may lead to a reduction of health problems.

High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for the problem of quantizing a linear regressor learned from training data $(\mathbf{X}, \mathbf{y})$, for some underlying statistical relationship $\mathbf{y} = \mathbf{X}\boldsymbol{\theta} + \mathbf{v}$. The learned model, which is an estimate of the latent parameter $\boldsymbol{\theta} \in \mathbb{R}^d$, is constrained to be representable using only $Bd$ bits, where $B \in (0, \infty)$ is a pre-specified budget and $d$ is the dimension. We derive an information-theoretic lower bound for the minimax risk under this setting and propose a matching upper bound using randomized embedding-based algorithms which is tight up to constant factors. The lower and upper bounds together characterize the minimum threshold bit-budget required to achieve a performance risk comparable to the unquantized setting. We also propose randomized Hadamard embeddings that are computationally efficient and are optimal up to a mild logarithmic factor of the lower bound. Our model quantization strategy can be generalized and we show its efficacy by extending the method and upper-bounds to two-layer ReLU neural networks for non-linear regression. Numerical simulations show the improved performance of our proposed scheme as well as its closeness to the lower bound.

Active regression considers a linear regression problem where the learner receives a large number of data points but can only observe a small number of labels. Since online algorithms can deal with incremental training data and take advantage of low computational cost, we consider an online extension of the active regression problem: the learner receives data points one by one and immediately decides whether it should collect the corresponding labels. The goal is to efficiently maintain the regression of received data points with a small budget of label queries. We propose novel algorithms for this problem under $\ell_p$ loss where $p\in[1,2]$. To achieve a $(1+\epsilon)$-approximate solution, our proposed algorithms only require $\tilde{\mathcal{O}}(\epsilon^{-1} d \log(n\kappa))$ queries of labels, where $n$ is the number of data points and $\kappa$ is a quantity, called the condition number, of the data points. The numerical results verify our theoretical results and show that our methods have comparable performance with offline active regression algorithms.

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can perform poorly, leading to work in metric learning. However, being able to learn a similarity-sensitive distance function also presupposes access to a rich, discriminative representation for the objects at hand. In this dissertation we present contributions towards both ends. In the first part of the thesis, assuming good representations for the data, we present a formulation for metric learning that makes a more direct attempt to optimize for the k-NN accuracy as compared to prior work. We also present extensions of this formulation to metric learning for kNN regression, asymmetric similarity learning and discriminative learning of Hamming distance. In the second part, we consider a situation where we are on a limited computational budget i.e. optimizing over a space of possible metrics would be infeasible, but access to a label aware distance metric is still desirable. We present a simple, and computationally inexpensive approach for estimating a well motivated metric that relies only on gradient estimates, discussing theoretical and experimental results. In the final part, we address representational issues, considering group equivariant convolutional neural networks (GCNNs). Equivariance to symmetry transformations is explicitly encoded in GCNNs; a classical CNN being the simplest example. In particular, we present a SO(3)-equivariant neural network architecture for spherical data, that operates entirely in Fourier space, while also providing a formalism for the design of fully Fourier neural networks that are equivariant to the action of any continuous compact group.

We demonstrate an end-to-end framework to improve the resilience of man-made systems to unforeseen events. The framework is based on a physics-based digital twin model and three modules tasked with real-time fault diagnosis, prognostics and reconfiguration. The fault diagnosis module uses model-based diagnosis algorithms to detect and isolate faults and generates interventions in the system to disambiguate uncertain diagnosis solutions. We scale up the fault diagnosis algorithm to the required real-time performance through the use of parallelization and surrogate models of the physics-based digital twin. The prognostics module tracks the fault progressions and trains the online degradation models to compute remaining useful life of system components. In addition, we use the degradation models to assess the impact of the fault progression on the operational requirements. The reconfiguration module uses PDDL-based planning endowed with semantic attachments to adjust the system controls so that the fault impact on the system operation is minimized. We define a resilience metric and use the example of a fuel system model to demonstrate how the metric improves with our framework.

Algorithms used in the process of machine learning have a number of different functions. They are often used to map data, make sense of large quantities of data, and predict developments over time. There are few algorithms which can conceivably perform all three tasks. One of these is linear regression. This algorithm was originally developed for statistical processing the 19th century.

In this paper we present a general framework for estimating regression models subject to a user-defined level of fairness. We enforce fairness as a model selection step in which we choose the value of a ridge penalty to control the effect of sensitive attributes. We then estimate the parameters of the model conditional on the chosen penalty value. Our proposal is mathematically simple, with a solution that is partly in closed form, and produces estimates of the regression coefficients that are intuitive to interpret as a function of the level of fairness. Furthermore, it is easily extended to generalised linear models, kernelised regression models and other penalties; and it can accommodate multiple definitions of fairness. We compare our approach with the regression model from Komiyama et al. (2018), which implements a provably-optimal linear regression model; and with the fair models from Zafar et al. (2019). We evaluate these approaches empirically on six different data sets, and we find that our proposal provides better goodness of fit and better predictive accuracy for the same level of fairness. In addition, we highlight a source of bias in the original experimental evaluation in Komiyama et al. (2018).

Learning-to-rank, a machine learning technique widely used in information retrieval, has recently been applied to the problem of ligand-based virtual screening, to accelerate the early stages of new drug development. Ranking prediction models learn based on ordinal relationships, making them suitable for integrating assay data from various environments. Existing studies of rank prediction in compound screening have generally used a learning-to-rank method called RankSVM. However, they have not been compared with or validated against the gradient boosting decision tree (GBDT)-based learning-to-rank methods that have gained popularity recently. Furthermore, although the ranking metric called Normalized Discounted Cumulative Gain (NDCG) is widely used in information retrieval, it only determines whether the predictions are better than those of other models. In other words, NDCG is incapable of recognizing when a prediction model produces worse than random results. Nevertheless, NDCG is still used in the performance evaluation of compound screening using learning-to-rank. This study used the GBDT model with ranking loss functions, called lambdarank and lambdaloss, for ligand-based virtual screening; results were compared with existing RankSVM methods and GBDT models using regression. We also proposed a new ranking metric, Normalized Enrichment Discounted Cumulative Gain (NEDCG), which aims to properly evaluate the goodness of ranking predictions. Results showed that the GBDT model with learning-to-rank outperformed existing regression methods using GBDT and RankSVM on diverse datasets. Moreover, NEDCG showed that predictions by regression were comparable to random predictions in multi-assay, multi-family datasets, demonstrating its usefulness for a more direct assessment of compound screening performance.

Many automatic speech recognition (ASR) data sets include a single pre-defined test set consisting of one or more speakers whose speech never appears in the training set. This "hold-speaker(s)-out" data partitioning strategy, however, may not be ideal for data sets in which the number of speakers is very small. This study investigates ten different data split methods for five languages with minimal ASR training resources. We find that (1) model performance varies greatly depending on which speaker is selected for testing; (2) the average word error rate (WER) across all held-out speakers is comparable not only to the average WER over multiple random splits but also to any given individual random split; (3) WER is also generally comparable when the data is split heuristically or adversarially; (4) utterance duration and intensity are comparatively more predictive factors of variability regardless of the data split. These results suggest that the widely used hold-speakers-out approach to ASR data partitioning can yield results that do not reflect model performance on unseen data or speakers. Random splits can yield more reliable and generalizable estimates when facing data sparsity.

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on the coefficients and kernels are assumed to be indefinite. The algorithm involves two stages of sampling, the first stage sample consists of distributions and the second stage sample is obtained from these distributions. Asymptotic behaviors of the algorithm in different regularity ranges of the regression function are comprehensively studied and learning rates are derived via integral operator techniques. We get the optimal rates under some mild conditions, which matches the one-stage sampled minimax optimal rate. Compared with the kernel methods for distribution regression in the literature, the algorithm under consideration does not require the kernel to be symmetric and positive semi-definite and hence provides a simple paradigm for designing indefinite kernel methods, which enriches the theme of the distribution regression. To the best of our knowledge, this is the first result for distribution regression with indefinite kernels, and our algorithm can improve the saturation effect.