The development of high-throughput sequencing technologies has led to the production of largescale molecular profiling data, allowing us to gain insights into underlying biological processes (Wid lak, 2013). One such technology is microarray sequencing, in which mRNA counts are used to describe gene expression. Such data, known as transcriptomics, are widely used in the biomedical domain and when analyzed alongside survival times have provided extraordinary opportunities for biomarker characterization and prognostic modelling (Bøvelstad et al., 2007; Lloyd et al., 2015; Lightbody et al., 2019; Lu et al., 2021). However, profiling data is often high-dimensional, which introduces several statistical challenges including: (i) variable selection, (ii) effect estimation of the features, and (iii) scalable computation. The task of variable selection is particularly important, as few genes typically have an effect on the outcome. Motivated by clinical applicability, we propose a state-of-the-art scalable (variational) Bayesian variable selection method for the proportional hazards models. In recent years, several methods have been proposed to analyze sparse high-dimensional data, with one of the most popular being the LASSO (Tibshirani, 1996). As biomedical studies are often concerned with clinical phenotypes, such as time to disease recurrence or overall survival time, these methods have been adapted to support survival analysis (Antoniadis et al., 2010; Witten and Tibshirani, 2010). For instance, the LASSO, ridge and elastic-net penalties have all been extended to the proportional hazards model (Tibshirani, 1997; Gui and Li, 2005; Zou and Hastie, 2005; Simon et al., 2011).

Fuzzy inference engine, as one of the most important components of fuzzy systems, can obtain some meaningful outputs from fuzzy sets on input space and fuzzy rule base using fuzzy logic inference methods. In order to enhance the computational efficiency of fuzzy inference engine in multi-input-single-output (MISO) fuzzy systems, this paper aims mainly to investigate three MISO fuzzy hierarchial inference engines based on fuzzy implications satisfying the law of importation with aggregation functions (LIA). We firstly find some aggregation functions for well-known fuzzy implications such that they satisfy (LIA) with them. For a given aggregation function, the fuzzy implication which satisfies (LIA) with this aggregation function is then characterized. Finally, we construct three fuzzy hierarchical inference engines in MISO fuzzy systems applying aforementioned theoretical developments.

This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its instance-wise predictions. This is essential for critical applications, optimal decision making, cost-sensitive classification, and for some types of context change. Calibration research has a rich history which predates the birth of machine learning as an academic field by decades. However, a recent increase in the interest on calibration has led to new methods and the extension from binary to the multiclass setting. The space of options and issues to consider is large, and navigating it requires the right set of concepts and tools. We provide both introductory material and up-to-date technical details of the main concepts and methods, including proper scoring rules and other evaluation metrics, visualisation approaches, a comprehensive account of post-hoc calibration methods for binary and multiclass classification, and several advanced topics.

Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Here, fields denote physical quantities that change continuously as a function of space (and time) and information theory refers to Bayesian probabilistic logic equipped with the associated entropic information measures. Reconstructing a signal with IFT is a computational problem similar to training a generative neural network (GNN). In this paper, the inference in IFT is reformulated in terms of GNN training and the cross-fertilization of numerical variational inference methods used in IFT and machine learning are discussed. The discussion suggests that IFT inference can be regarded as a specific form of artificial intelligence. In contrast to classical neural networks, IFT based GNNs can operate without pre-training thanks to incorporating expert knowledge into their architecture.

Independent component analysis is intended to recover the unknown components as independent as possible from their linear mixtures. This technique has been widely used in many fields, such as data analysis, signal processing, and machine learning. In this paper, we present a novel boosting-based algorithm for independent component analysis. Our algorithm fills the gap in the nonparametric independent component analysis by introducing boosting to maximum likelihood estimation. A variety of experiments validate its performance compared with many of the presently known algorithms.

We consider a seller offering a large network of $N$ products over a time horizon of $T$ periods. The seller does not know the parameters of the products' linear demand model, and can dynamically adjust product prices to learn the demand model based on sales observations. The seller aims to minimize its pseudo-regret, i.e., the expected revenue loss relative to a clairvoyant who knows the underlying demand model. We consider a sparse set of demand relationships between products to characterize various connectivity properties of the product network. In particular, we study three different sparsity frameworks: (1) $L_0$ sparsity, which constrains the number of connections in the network, and (2) off-diagonal sparsity, which constrains the magnitude of cross-product price sensitivities, and (3) a new notion of spectral sparsity, which constrains the asymptotic decay of a similarity metric on network nodes. We propose a dynamic pricing-and-learning policy that combines the optimism-in-the-face-of-uncertainty and PAC-Bayesian approaches, and show that this policy achieves asymptotically optimal performance in terms of $N$ and $T$. We also show that in the case of spectral and off-diagonal sparsity, the seller can have a pseudo-regret linear in $N$, even when the network is dense.

This paper addresses and solves some challenges in the adoption of machine learning in insurance with the democratization of model deployment. The first challenge is reducing the labelling effort (hence focusing on the data quality) with the help of active learning, a feedback loop between the model inference and an oracle: as in insurance the unlabeled data is usually abundant, active learning can become a significant asset in reducing the labelling cost. For that purpose, this paper sketches out various classical active learning methodologies before studying their empirical impact on both synthetic and real datasets. Another key challenge in insurance is the fairness issue in model inferences. We will introduce and integrate a post-processing fairness for multi-class tasks in this active learning framework to solve these two issues. Finally numerical experiments on unfair datasets highlight that the proposed setup presents a good compromise between model precision and fairness.

We formally map the problem of sampling from an unknown distribution with density $p_X$ in $\mathbb{R}^d$ to the problem of learning and sampling $p_\mathbf{Y}$ in $\mathbb{R}^{Md}$ obtained by convolving $p_X$ with a fixed factorial kernel: $p_\mathbf{Y}$ is referred to as M-density and the factorial kernel as multimeasurement noise model (MNM). The M-density is smoother than $p_X$, easier to learn and sample from, yet for large $M$ the two problems are mathematically equivalent since $X$ can be estimated exactly given $\mathbf{Y}=\mathbf{y}$ using the Bayes estimator $\widehat{x}(\mathbf{y})=\mathbb{E}[X\vert\mathbf{Y}=\mathbf{y}]$. To formulate the problem, we derive $\widehat{x}(\mathbf{y})$ for Poisson and Gaussian MNMs expressed in closed form in terms of unnormalized $p_\mathbf{Y}$. This leads to a simple least-squares objective for learning parametric energy and score functions. We present various parametrization schemes of interest, including one in which studying Gaussian M-densities directly leads to multidenoising autoencoders--this is the first theoretical connection made between denoising autoencoders and empirical Bayes in the literature. Samples from $p_X$ are obtained by walk-jump sampling (Saremi & Hyvarinen, 2019) via underdamped Langevin MCMC (walk) to sample from $p_\mathbf{Y}$ and the multimeasurement Bayes estimation of $X$ (jump). We study permutation invariant Gaussian M-densities on MNIST, CIFAR-10, and FFHQ-256 datasets, and demonstrate the effectiveness of this framework for realizing fast-mixing stable Markov chains in high dimensions.

Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well understood than OT. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples and simulations validating theoretical results.

A natural strategy for mitigating the curse of dimensionality in estimating probability distributions is to employ lowcomplexity family of approximation distributions. For discrete distributions, Chow and Liu [5] suggested a family of tree-based approximations and gave an efficient maximum-likelihood estimator based on Kruskal's optimal spanning tree algorithm [14]. We stress that this approach makes no structural assumptions about the sampling distribution, but rather constitutes a modeling choice. Consequently, in this paradigm, the goal is to approximate the optimal-tree distribution from the data, without any guarantees on how well the latter approximates the true sampling distribution. Extensions of the Chow-Liu approach to continuous distributions were studied by Bach and Jordan [1] and by Liu et al. [16] under various assumptions.