Single-cell RNA sequencing allows the quantitation of gene expression at the individual cell level, enabling the study of cellular heterogeneity and gene expression dynamics. Dimensionality reduction is a common preprocessing step to simplify the visualization, clustering, and phenotypic characterization of samples. This step, often performed using principal component analysis or closely related methods, is challenging because of the size and complexity of the data. In this work, we present a generalized matrix factorization model assuming a general exponential dispersion family distribution and we show that many of the proposed approaches in the single-cell dimensionality reduction literature can be seen as special cases of this model. Furthermore, we propose a scalable adaptive stochastic gradient descent algorithm that allows us to estimate the model efficiently, enabling the analysis of millions of cells. Our contribution extends to introducing a novel warm start initialization method, designed to accelerate algorithm convergence and increase the precision of final estimates. Moreover, we discuss strategies for dealing with missing values and model selection. We benchmark the proposed algorithm through extensive numerical experiments against state-of-the-art methods and showcase its use in real-world biological applications. The proposed method systematically outperforms existing methods of both generalized and non-negative matrix factorization, demonstrating faster execution times while maintaining, or even enhancing, matrix reconstruction fidelity and accuracy in biological signal extraction. Finally, all the methods discussed here are implemented in an efficient open-source R package, sgdGMF, available at github/CristianCastiglione/sgdGMF

Compared to "black-box" models, like random forests and deep neural networks, explainable boosting machines (EBMs) are considered "glass-box" models that can be competitively accurate while also maintaining a higher degree of transparency and explainability. However, EBMs become readily less transparent and harder to interpret in high-dimensional settings with many predictor variables; they also become more difficult to use in production due to increases in scoring time. We propose a simple solution based on the least absolute shrinkage and selection operator (LASSO) that can help introduce sparsity by reweighting the individual model terms and removing the less relevant ones, thereby allowing these models to maintain their transparency and relatively fast scoring times in higher-dimensional settings. In short, post-processing a fitted EBM with many (i.e., possibly hundreds or thousands) of terms using the LASSO can help reduce the model's complexity and drastically improve scoring time. We illustrate the basic idea using two real-world examples with code.

Insurers usually turn to generalized linear models for modelling claim frequency and severity data. Due to their success in other fields, machine learning techniques are gaining popularity within the actuarial toolbox. Our paper contributes to the literature on frequency-severity insurance pricing with machine learning via deep learning structures. We present a benchmark study on four insurance data sets with frequency and severity targets in the presence of multiple types of input features. We compare in detail the performance of: a generalized linear model on binned input data, a gradient-boosted tree model, a feed-forward neural network (FFNN), and the combined actuarial neural network (CANN). Our CANNs combine a baseline prediction established with a GLM and GBM, respectively, with a neural network correction. We explain the data preprocessing steps with specific focus on the multiple types of input features typically present in tabular insurance data sets, such as postal codes, numeric and categorical covariates. Autoencoders are used to embed the categorical variables into the neural network and we explore their potential advantages in a frequency-severity setting. Finally, we construct global surrogate models for the neural nets' frequency and severity models. These surrogates enable the translation of the essential insights captured by the FFNNs or CANNs to GLMs. As such, a technical tariff table results that can easily be deployed in practice.

Multiple data views measured on the same set of participants is becoming more common and has the potential to deepen our understanding of many complex diseases by analyzing these different views simultaneously. Equally important, many of these complex diseases show evidence of subgroup heterogeneity (e.g., by sex or race). HIP (Heterogeneity in Integration and Prediction) is among the first methods proposed to integrate multiple data views while also accounting for subgroup heterogeneity to identify common and subgroup-specific markers of a particular disease. However, HIP is applicable to continuous outcomes and requires programming expertise by the user. Here we propose extensions to HIP that accommodate multi-class, Poisson, and Zero-Inflated Poisson outcomes while retaining the benefits of HIP. Additionally, we introduce an R Shiny application, accessible on shinyapps.io at https://multi-viewlearn.shinyapps.io/HIP_ShinyApp/, that provides an interface with the Python implementation of HIP to allow more researchers to use the method anywhere and on any device. We applied HIP to identify genes and proteins common and specific to males and females that are associated with exacerbation frequency. Although some of the identified genes and proteins show evidence of a relationship with chronic obstructive pulmonary disease (COPD) in existing literature, others may be candidates for future research investigating their relationship with COPD. We demonstrate the use of the Shiny application with a publicly available data. An R-package for HIP would be made available at https://github.com/lasandrall/HIP.

One of the main tasks of actuaries and data scientists is to build good predictive models for certain phenomena such as the claim size or the number of claims in insurance. These models ideally exploit given feature information to enhance the accuracy of prediction. This user guide revisits and clarifies statistical techniques to assess the calibration or adequacy of a model on the one hand, and to compare and rank different models on the other hand. In doing so, it emphasises the importance of specifying the prediction target functional at hand a priori (e.g. the mean or a quantile) and of choosing the scoring function in model comparison in line with this target functional. Guidance for the practical choice of the scoring function is provided. Striving to bridge the gap between science and daily practice in application, it focuses mainly on the pedagogical presentation of existing results and of best practice. The results are accompanied and illustrated by two real data case studies on workers' compensation and customer churn.

Passengers respond heterogeneously to such disruptive events based on numerous factors. This study takes a data-driven approach to explore multi-modal demand dynamics under disruptions. We first develop a methodology to automatically detect anomalous instances through historical hourly travel demand data. Then we apply clustering to these anomalous hours to distinguish various forms of multi-modal demand dynamics occurring during disruptions. Our study provides a straightforward tool for categorising various passenger responses to disruptive events in terms of mode choice and paves the way for predictive analyses on estimating the scope of modal shift under distinct disruption scenarios.

Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be considered to preserve the complete information of the original data and limit the dimensionality. Dimensionality reduction and feature selection are common preprocessing techniques addressing the challenge of efficiently dealing with high-dimensional data. Dimensionality reduction methods control the number of features in the dataset while preserving its structure and minimizing information loss. Feature selection aims to identify the most relevant features for a task, discarding the less informative ones. Previous works have proposed approaches that aggregate features depending on their correlation without discarding any of them and preserving their interpretability through aggregation with the mean. A limitation of methods based on correlation is the assumption of linearity in the relationship between features and target. In this paper, we relax such an assumption in two ways. First, we propose a bias-variance analysis for general models with additive Gaussian noise, leading to a dimensionality reduction algorithm (NonLinCFA) which aggregates non-linear transformations of features with a generic aggregation function. Then, we extend the approach assuming that a generalized linear model regulates the relationship between features and target. A deviance analysis leads to a second dimensionality reduction algorithm (GenLinCFA), applicable to a larger class of regression problems and classification settings. Finally, we test the algorithms on synthetic and real-world datasets, performing regression and classification tasks, showing competitive performances.

Changes in real-world dynamic processes are often described in terms of differences in energies $\textbf{E}(\underline{\alpha})$ of a set of spectral-bands $\underline{\alpha}$. Given continuous spectra of two classes $A$ and $B$, or in general, two stochastic processes $S^{(A)}(f)$ and $S^{(B)}(f)$, $f \in \mathbb{R}^+$, we address the ubiquitous problem of identifying a subset of intervals of $f$ called spectral-bands $\underline{\alpha} \subset \mathbb{R}^+$ such that the energies $\textbf{E}(\underline{\alpha})$ of these bands can optimally discriminate between the two classes. We introduce EGO-MDA, an unsupervised method to identify optimal spectral-bands $\underline{\alpha}^*$ for given samples of spectra from two classes. EGO-MDA employs a statistical approach that iteratively minimizes an adjusted multinomial log-likelihood (deviance) criterion $\mathcal{D}(\underline{\alpha},\mathcal{M})$. Here, Mixture Discriminant Analysis (MDA) aims to derive MLE of two GMM distribution parameters, i.e., $\mathcal{M}^* = \underset{\mathcal{M}}{\rm argmin}~\mathcal{D}(\underline{\alpha}, \mathcal{M})$ and identify a classifier that optimally discriminates between two classes for a given spectral representation. The Efficient Global Optimization (EGO) finds the spectral-bands $\underline{\alpha}^* = \underset{\underline{\alpha}}{\rm argmin}~\mathcal{D}(\underline{\alpha},\mathcal{M})$ for given GMM parameters $\mathcal{M}$. For pathological cases of low separation between mixtures and model misspecification, we discuss the effect of the sample size and the number of iterations on the estimates of parameters $\mathcal{M}$ and therefore the classifier performance. A case study on a synthetic data set is provided. In an engineering application of optimal spectral-banding for anomaly tracking, EGO-MDA achieved at least 70% improvement in the median deviance relative to other methods tested.

Log and square root transformations of target variable are routinely used in forecasting models to predict future sales. These transformations often lead to better performing models. However, they also introduce a systematic negative bias (under-forecasting). In this paper, we demonstrate the existence of this bias, dive deep into its root cause and introduce two methods to correct for the bias. We conclude that the proposed bias correction methods improve model performance (by up to 50%) and make a case for incorporating bias correction in modeling workflow. We also experiment with `Tweedie' family of cost functions which circumvents the transformation bias issue by modeling directly on sales. We conclude that Tweedie regression gives the best performance so far when modeling on sales making it a strong alternative to working with a transformed target variable.

Before we discuss deviance, we first need to understand what the Saturated, Proposed and Null Models are. A Saturated Model is where the number of parameters/coefficients is equal to the number of data points. This is like a'connect the dots' model where the line or curve passes through each point. This is considered to be the perfect model as it takes into account all the variance in the data and has the maximum achievable likelihood. A Null Model is the opposite with only one parameter, which is the intercept.