How to solve high-dimensional linear programs (LPs) efficiently is a fundamental question. Recently, there has been a surge of interest in reducing LP sizes using \textit{random projections}, which can accelerate solving LPs independently of improving LP solvers. In this paper, we explore a new direction of \emph{data-driven projections}, which use projection matrices learned from data instead of random projection matrices. Given data of past $n$-dimensional LPs, we learn an $n\times k$ projection matrix such that $n > k$. When addressing a future LP instance, we reduce its dimensionality from $n$ to $k$ via the learned projection matrix, solve the resulting LP to obtain a $k$-dimensional solution, and apply the learned matrix to it to recover an $n$-dimensional solution. On the theoretical side, a natural question is: how much data is sufficient to ensure the quality of recovered solutions? We address this question based on the framework of \textit{data-driven algorithm design}, which connects the amount of data sufficient for establishing generalization bounds to the \textit{pseudo-dimension} of performance metrics. We obtain an $\tilde{\mathrm{O}}(nk^2)$ upper bound on the pseudo-dimension, where $\tilde{\mathrm{O}}$ compresses logarithmic factors. We also provide an $\Omega(nk)$ lower bound, implying our result is tight up to an $\tilde{\mathrm{O}}(k)$ factor. On the practical side, we explore two natural methods for learning projection matrices: PCA- and gradient-based methods. While the former is simple and efficient, the latter can sometimes lead to better solution quality. Our experiments confirm the practical benefit of learning projection matrices from data, achieving significantly higher solution quality than the existing random projection while greatly reducing the time for solving LPs.

Datasets with an equal number of samples per class, such as MNIST [Lecun et al., 1998], CIFAR10, and CIFAR100 [Krizhevsky, 2009], are often used, when we evaluate classification models and training methods in machine learning. However, it is empirically known that the size distribution in the real world often shows a type of exponential distribution called Pareto distribution [Reed, 2001], and the same is true for the number of per-class samples in classification problems [Li et al., 2017, Spain and Perona, 2007]. Such distributions are called long-tailed data due to the shape of the distribution since some classes (head classes) are often sampled and many others (tail classes) are not sampled very often. Long-tailed recognition (LTR) is used to attempt to improve the accuracy of classification models on uniform distribution when training data shows such a distribution. There is a problem in LTR that the head classes have large sample size; thus, the output is biased toward them. This reduces the overall and tail class accuracy because tail classes make up the majority [Zhang et al., 2021]. Various methods have been developed for LTR, such as class-balanced loss (CB) [Cui et al., 2019], augmenting samples of tail classes [Wang et al., 2021], two-stage learning [Kang et al.,

Machine learning typically presupposes classical probability theory which implies that aggregation is built upon expectation. There are now multiple reasons to motivate looking at richer alternatives to classical probability theory as a mathematical foundation for machine learning. We systematically examine a powerful and rich class of alternative aggregation functionals, known variously as spectral risk measures, Choquet integrals or Lorentz norms. We present a range of characterization results, and demonstrate what makes this spectral family so special. In doing so we arrive at a natural stratification of all coherent risk measures in terms of the upper probabilities that they induce by exploiting results from the theory of rearrangement invariant Banach spaces. We empirically demonstrate how this new approach to uncertainty helps tackling practical machine learning problems.

The future of transportation is being shaped by technology, and one revolutionary step in improving road safety is the incorporation of robotic systems into driver monitoring infrastructure. This literature review explores the current landscape of driver monitoring systems, ranging from traditional physiological parameter monitoring to advanced technologies such as facial recognition to steering analysis. Exploring the challenges faced by existing systems, the review then investigates the integration of robots as intelligent entities within this framework. These robotic systems, equipped with artificial intelligence and sophisticated sensors, not only monitor but actively engage with the driver, addressing cognitive and emotional states in real-time. The synthesis of existing research reveals a dynamic interplay between human and machine, offering promising avenues for innovation in adaptive, personalized, and ethically responsible human-robot interactions for driver monitoring. This review establishes a groundwork for comprehending the intricacies and potential avenues within this dynamic field. It encourages further investigation and advancement at the intersection of human-robot interaction and automotive safety, introducing a novel direction. This involves various sections detailing technological enhancements that can be integrated to propose an innovative and improved driver monitoring system.

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used dimension reduction technique, it lacks robustness with respect to these transformations. Modern alternatives, such as autoencoders, can be invariant with respect to specific transformations but are generally not interpretable. We introduce General Transform-Invariant Principal Component Analysis (GT-PCA) as an effective and interpretable alternative to PCA and autoencoders. We propose a neural network that efficiently estimates the components and show that GT-PCA significantly outperforms alternative methods in experiments based on synthetic and real data.

Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed in a series of papers and it has a wide range of applications, from general linear systems, even in a closed-loop setup, to nonlinear and nonparametric approaches. Although several theoretical properties of SPS were proven in the literature, the sample complexity of the method was not analysed so far. This paper aims to fill this gap and provides the first results on the sample complexity of SPS. Here, we focus on scalar linear regression problems, that is we study the behaviour of SPS confidence intervals. We provide high probability upper bounds, under three different sets of assumptions, showing that the sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if the observation noises are subgaussian. We also show that similar bounds hold for the previously proposed outer approximation of the confidence region. Finally, we present simulation experiments comparing the theoretical and the empirical convergence rates.

Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation hyperparameter, and especially in the context of high-dimensional data. We present a prevalidated ridge regression model that closely matches logistic regression in terms of classification error and log-loss, particularly for high-dimensional data, while being significantly more computationally efficient and having effectively no hyperparameters beyond regularisation. We scale the coefficients of the model so as to minimise log-loss for a set of prevalidated predictions derived from the estimated leave-one-out cross-validation error. This exploits quantities already computed in the course of fitting the ridge regression model in order to find the scaling parameter with nominal additional computational expense.

Most existing personalized federated learning approaches are based on intricate designs, which often require complex implementation and tuning. In order to address this limitation, we propose a simple yet effective personalized federated learning framework. Specifically, during each communication round, we group clients into multiple clusters based on their model training status and data distribution on the server side. We then consider each cluster center as a node equipped with model parameters and construct a graph that connects these nodes using weighted edges. Additionally, we update the model parameters at each node by propagating information across the entire graph. Subsequently, we design a precise personalized model distribution strategy to allow clients to obtain the most suitable model from the server side. We conduct experiments on three image benchmark datasets and create synthetic structured datasets with three types of typologies. Experimental results demonstrate the effectiveness of the proposed work.

This paper addresses a multi-echelon inventory management problem with a complex network topology where deriving optimal ordering decisions is difficult. Deep reinforcement learning (DRL) has recently shown potential in solving such problems, while designing the neural networks in DRL remains a challenge. In order to address this, a DRL model is developed whose Q-network is based on radial basis functions. The approach can be more easily constructed compared to classic DRL models based on neural networks, thus alleviating the computational burden of hyperparameter tuning. Through a series of simulation experiments, the superior performance of this approach is demonstrated compared to the simple base-stock policy, producing a better policy in the multi-echelon system and competitive performance in the serial system where the base-stock policy is optimal. In addition, the approach outperforms current DRL approaches.

Many tasks in explainable machine learning, such as data valuation and feature attribution, perform expensive computation for each data point and can be intractable for large datasets. These methods require efficient approximations, and learning a network that directly predicts the desired output, which is commonly known as amortization, is a promising solution. However, training such models with exact labels is often intractable; we therefore explore training with noisy labels and find that this is inexpensive and surprisingly effective. Through theoretical analysis of the label noise and experiments with various models and datasets, we show that this approach significantly accelerates several feature attribution and data valuation methods, often yielding an order of magnitude speedup over existing approaches.