The cubic regularization method (CR) is a popular algorithm for unconstrained non-convex optimization. At each iteration, CR solves a cubically regularized quadratic problem, called the cubic regularization subproblem (CRS). One way to solve the CRS relies on solving the secular equation, whose computational bottleneck lies in the computation of all eigenvalues of the Hessian matrix. In this paper, we propose and analyze a novel CRS solver based on an approximate secular equation, which requires only some of the Hessian eigenvalues and is therefore much more efficient. Two approximate secular equations (ASEs) are developed. For both ASEs, we first study the existence and uniqueness of their roots and then establish an upper bound on the gap between the root and that of the standard secular equation. Such an upper bound can in turn be used to bound the distance from the approximate CRS solution based ASEs to the true CRS solution, thus offering a theoretical guarantee for our CRS solver. A desirable feature of our CRS solver is that it requires only matrix-vector multiplication but not matrix inversion, which makes it particularly suitable for high-dimensional applications of unconstrained non-convex optimization, such as low-rank recovery and deep learning. Numerical experiments with synthetic and real data-sets are conducted to investigate the practical performance of the proposed CRS solver. Experimental results show that the proposed solver outperforms two state-of-the-art methods.

Stochastic optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. Although various algorithms have been extensively studied for AUPRC optimization, the generalization is only guaranteed in the multi-query case. In this work, we present the first trial in the single-query generalization of stochastic AUPRC optimization. For sharper generalization bounds, we focus on algorithm-dependent generalization. There are both algorithmic and theoretical obstacles to our destination. From an algorithmic perspective, we notice that the majority of existing stochastic estimators are biased only when the sampling strategy is biased, and is leave-one-out unstable due to the non-decomposability. To address these issues, we propose a sampling-rate-invariant unbiased stochastic estimator with superior stability. On top of this, the AUPRC optimization is formulated as a composition optimization problem, and a stochastic algorithm is proposed to solve this problem. From a theoretical perspective, standard techniques of the algorithm-dependent generalization analysis cannot be directly applied to such a listwise compositional optimization problem. To fill this gap, we extend the model stability from instancewise losses to listwise losses and bridge the corresponding generalization and stability. Additionally, we construct state transition matrices to describe the recurrence of the stability, and simplify calculations by matrix spectrum. Practically, experimental results on three image retrieval datasets on speak to the effectiveness and soundness of our framework.

Although overparameterized models have shown their success on many machine learning tasks, the accuracy could drop on the testing distribution that is different from the training one. This accuracy drop still limits applying machine learning in the wild. At the same time, importance weighting, a traditional technique to handle distribution shifts, has been demonstrated to have less or even no effect on overparameterized models both empirically and theoretically. In this paper, we propose importance tempering to improve the decision boundary and achieve consistently better results for overparameterized models. Theoretically, we justify that the selection of group temperature can be different under label shift and spurious correlation setting. At the same time, we also prove that properly selected temperatures can extricate the minority collapse for imbalanced classification. Empirically, we achieve state-of-the-art results on worst group classification tasks using importance tempering.

COVID-19 poses disproportionate mental health consequences to the public during different phases of the pandemic. We use a computational approach to capture the specific aspects that trigger an online community's anxiety about the pandemic and investigate how these aspects change over time. First, we identified nine subjects of anxiety (SOAs) in a sample of Reddit posts ($N$=86) from r/COVID19\_support using thematic analysis. Then, we quantified Reddit users' anxiety by training algorithms on a manually annotated sample ($N$=793) to automatically label the SOAs in a larger chronological sample ($N$=6,535). The nine SOAs align with items in various recently developed pandemic anxiety measurement scales. We observed that Reddit users' concerns about health risks remained high in the first eight months of the pandemic. These concerns diminished dramatically despite the surge of cases occurring later. In general, users' language disclosing the SOAs became less intense as the pandemic progressed. However, worries about mental health and the future increased steadily throughout the period covered in this study. People also tended to use more intense language to describe mental health concerns than health risks or death concerns. Our results suggest that this online group's mental health condition does not necessarily improve despite COVID-19 gradually weakening as a health threat due to appropriate countermeasures. Our system lays the groundwork for population health and epidemiology scholars to examine aspects that provoke pandemic anxiety in a timely fashion.

Previous analysis has been performed on the daily number of cases, deaths, infected people, and people who were exposed to the virus, all of them in a timeline of 550 days. Moreover, it has made the fitting of infection spread detailing the most efficient and optimal methods with lower propagation error and the presence of statistical biases. Finally, four different prevention scenarios were proposed to evaluate the ratio of each one of the parameters related to the disease.

In edge computing, suppressing data size is a challenge for machine learning models that perform complex tasks such as autonomous driving, in which computational resources (speed, memory size and power) are limited. Efficient lossy compression of matrix data has been introduced by decomposing it into the product of an integer and real matrices. However, its optimisation is difficult as it requires simultaneous optimisation of an integer and real variables. In this paper, we improve this optimisation by utilising recently developed black-box optimisation (BBO) algorithms with an Ising solver for integer variables. In addition, the algorithm can be used to solve mixed-integer programming problems that are linear and non-linear in terms of real and integer variables, respectively. The differences between the choice of Ising solvers (simulated annealing, quantum annealing and simulated quenching) and the strategies of the BBO algorithms (BOCS, FMQA and their variations) are discussed for further development of the BBO techniques.

We present RuDSI, a new benchmark for word sense induction (WSI) in Russian. The dataset was created using manual annotation and semi-automatic clustering of Word Usage Graphs (WUGs). Unlike prior WSI datasets for Russian, RuDSI is completely data-driven (based on texts from Russian National Corpus), with no external word senses imposed on annotators. Depending on the parameters of graph clustering, different derivative datasets can be produced from raw annotation. We report the performance that several baseline WSI methods obtain on RuDSI and discuss possibilities for improving these scores.

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning settings, leading to unintuitive model interpretation. In particular, the Shapley value uses the same weight for all marginal contributions -- i.e. it gives the same importance when a large number of other features are given versus when a small number of other features are given. This property can be problematic if larger feature sets are more or less informative than smaller feature sets. Our work performs a rigorous analysis of the potential limitations of Shapley feature attribution. We identify simple settings where the Shapley value is mathematically suboptimal by assigning larger attributions for less influential features. Motivated by this observation, we propose WeightedSHAP, which generalizes the Shapley value and learns which marginal contributions to focus directly from data. On several real-world datasets, we demonstrate that the influential features identified by WeightedSHAP are better able to recapitulate the model's predictions compared to the features identified by the Shapley value.

Machine Learning permeates many industries, which brings new source of benefits for companies. However within the life insurance industry, Machine Learning is not widely used in practice as over the past years statistical models have shown their efficiency for risk assessment. Thus insurers may face difficulties to assess the value of the artificial intelligence. Focusing on the modification of the life insurance industry over time highlights the stake of using Machine Learning for insurers and benefits that it can bring by unleashing data value. This paper reviews traditional actuarial methodologies for survival modeling and extends them with Machine Learning techniques. It points out differences with regular machine learning models and emphasizes importance of specific implementations to face censored data with machine learning models family. In complement to this article, a Python library has been developed. Different open-source Machine Learning algorithms have been adjusted to adapt the specificities of life insurance data, namely censoring and truncation. Such models can be easily applied from this SCOR library to accurately model life insurance risks.

We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.