\texttt{Mixture-Models} is an open-source Python library for fitting Gaussian Mixture Models (GMM) and their variants, such as Parsimonious GMMs, Mixture of Factor Analyzers, MClust models, Mixture of Student's t distributions, etc. It streamlines the implementation and analysis of these models using various first/second order optimization routines such as Gradient Descent and Newton-CG through automatic differentiation (AD) tools. This helps in extending these models to high-dimensional data, which is first of its kind among Python libraries. The library provides user-friendly model evaluation tools, such as BIC, AIC, and log-likelihood estimation. The source-code is licensed under MIT license and can be accessed at \url{https://github.com/kasakh/Mixture-Models}. The package is highly extensible, allowing users to incorporate new distributions and optimization techniques with ease. We conduct a large scale simulation to compare the performance of various gradient based approaches against Expectation Maximization on a wide range of settings and identify the corresponding best suited approach.

Machine learning is a rapidly evolving field with a wide range of applications, including biological signal analysis, where novel algorithms often improve the state-of-the-art. However, robustness to algorithmic variability - measured by different algorithms, consistently uncovering similar findings - is seldom explored. In this paper we investigate whether established hypotheses in brain-age prediction from EEG research validate across algorithms. First, we surveyed literature and identified various features known to be informative for brain-age prediction. We employed diverse feature extraction techniques, processing steps, and models, and utilized the interpretative power of SHapley Additive exPlanations (SHAP) values to align our findings with the existing research in the field. Few of our models achieved state-of-the-art performance on the specific data-set we utilized. Moreover, analysis demonstrated that while most models do uncover similar patterns in the EEG signals, some variability could still be observed. Finally, a few prominent findings could only be validated using specific models. We conclude by suggesting remedies to the potential implications of this lack of robustness to model variability.

Estimation of heterogeneous treatment effects from observational data has become an important problem. It plays a crucial role in determining the individualized causal effects of a treatment, which then leads to a personalized assignment of optimal treatment (Wendling et al., 2018; Rekkas et al., 2020). Estimation of such heterogeneity however requires reasonable representations from each treatment subgroup. With the increasing availability of large-scale health outcome data such as electronic health records (EHR) data in recent years, it has become possible to develop individualized treatment strategies efficiently. This led to the development of several novel statistical methods, primarily tailored for binary treatment scenarios (Wendling et al., 2018; Cheng et al., 2020), with some accommodating multiple treatment settings (Brown et al., 2020; Chalkou et al., 2021). Most of these approaches are specifically designed for estimating population average treatment effects (ATEs) (Van Der Laan and Rubin, 2006; Chernozhukov et al., 2018; McCaffrey et al., 2013) and more recently, methods are being developed to estimate conditional average treatment effects (CATEs) (Taddy et al., 2016; Wager and Athey, 2018; Künzel et al., 2019; Nie and Wager, 2021). Here, we tackle a generic problem of heterogeneous treatment effect or CATE estimation in a multi-treatment setting, where the treatment responses may share some commonalities.

The rise of Artificial Intelligence (AI) has revolutionized numerous industries and transformed the way society operates. Its widespread use has led to the distribution of AI and its underlying data across many intelligent systems. In this light, it is crucial to utilize information in learning processes that are either distributed or owned by different entities. As a result, modern data-driven services have been developed to integrate distributed knowledge entities into their outcomes. In line with this goal, the latest AI models are frequently trained in a decentralized manner. Distributed learning involves multiple entities working together to make collective predictions and decisions. However, this collaboration can also bring about security vulnerabilities and challenges. This paper provides an in-depth survey on private knowledge sharing in distributed learning, examining various knowledge components utilized in leading distributed learning architectures. Our analysis sheds light on the most critical vulnerabilities that may arise when using these components in a distributed setting. We further identify and examine defensive strategies for preserving the privacy of these knowledge components and preventing malicious parties from manipulating or accessing the knowledge information. Finally, we highlight several key limitations of knowledge sharing in distributed learning and explore potential avenues for future research.

Objective. Achieving appropriate spinopelvic alignment has been shown to be associated with improved clinical symptoms. However, measurement of spinopelvic radiographic parameters is time-intensive and interobserver reliability is a concern. Automated measurement tools have the promise of rapid and consistent measurements, but existing tools are still limited by some degree of manual user-entry requirements. This study presents a novel artificial intelligence (AI) tool called SpinePose that automatically predicts spinopelvic parameters with high accuracy without the need for manual entry. Methods. SpinePose was trained and validated on 761 sagittal whole-spine X-rays to predict sagittal vertical axis (SVA), pelvic tilt (PT), pelvic incidence (PI), sacral slope (SS), lumbar lordosis (LL), T1-pelvic angle (T1PA), and L1-pelvic angle (L1PA). A separate test set of 40 X-rays was labeled by 4 reviewers, including fellowship-trained spine surgeons and a fellowship-trained radiologist with neuroradiology subspecialty certification. Median errors relative to the most senior reviewer were calculated to determine model accuracy on test images. Intraclass correlation coefficients (ICC) were used to assess inter-rater reliability. Results. SpinePose exhibited the following median (interquartile range) parameter errors: SVA: 2.2(2.3)mm, p=0.93; PT: 1.3(1.2){\deg}, p=0.48; SS: 1.7(2.2){\deg}, p=0.64; PI: 2.2(2.1){\deg}, p=0.24; LL: 2.6(4.0){\deg}, p=0.89; T1PA: 1.1(0.9){\deg}, p=0.42; and L1PA: 1.4(1.6){\deg}, p=0.49. Model predictions also exhibited excellent reliability at all parameters (ICC: 0.91-1.0). Conclusions. SpinePose accurately predicted spinopelvic parameters with excellent reliability comparable to fellowship-trained spine surgeons and neuroradiologists. Utilization of predictive AI tools in spinal imaging can substantially aid in patient selection and surgical planning.

In the general framework of Bayesian inference, the target distribution can only be evaluated up-to a constant of proportionality. Classical consistent Bayesian methods such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) have unbounded time complexity requirements. We develop a fully parallel sequential Monte Carlo (pSMC) method which provably delivers parallel strong scaling, i.e. the time complexity (and per-node memory) remains bounded if the number of asynchronous processes is allowed to grow. More precisely, the pSMC has a theoretical convergence rate of MSE$ = O(1/NR)$, where $N$ denotes the number of communicating samples in each processor and $R$ denotes the number of processors. In particular, for suitably-large problem-dependent $N$, as $R \rightarrow \infty$ the method converges to infinitesimal accuracy MSE$=O(\varepsilon^2)$ with a fixed finite time-complexity Cost$=O(1)$ and with no efficiency leakage, i.e. computational complexity Cost$=O(\varepsilon^{-2})$. A number of Bayesian inference problems are taken into consideration to compare the pSMC and MCMC methods.

Mixup is a data augmentation strategy that employs convex combinations of training instances and their respective labels to augment the robustness and calibration of deep neural networks. Despite its widespread adoption, the nuanced mechanisms that underpin its success are not entirely understood. The observed phenomenon of Neural Collapse, where the last-layer activations and classifier of deep networks converge to a simplex equiangular tight frame (ETF), provides a compelling motivation to explore whether mixup induces alternative geometric configurations and whether those could explain its success. In this study, we delve into the last-layer activations of training data for deep networks subjected to mixup, aiming to uncover insights into its operational efficacy. Our investigation, spanning various architectures and dataset pairs, reveals that mixup's last-layer activations predominantly converge to a distinctive configuration different than one might expect. In this configuration, activations from mixed-up examples of identical classes align with the classifier, while those from different classes delineate channels along the decision boundary. Moreover, activations in earlier layers exhibit patterns, as if trained with manifold mixup. These findings are unexpected, as mixed-up features are not simple convex combinations of feature class means (as one might get, for example, by training mixup with the mean squared error loss). By analyzing this distinctive geometric configuration, we elucidate the mechanisms by which mixup enhances model calibration. To further validate our empirical observations, we conduct a theoretical analysis under the assumption of an unconstrained features model, utilizing the mixup loss. Through this, we characterize and derive the optimal last-layer features under the assumption that the classifier forms a simplex ETF.

We study off-policy learning (OPL) of contextual bandit policies in large discrete action spaces where existing methods -- most of which rely crucially on reward-regression models or importance-weighted policy gradients -- fail due to excessive bias or variance. To overcome these issues in OPL, we propose a novel two-stage algorithm, called Policy Optimization via Two-Stage Policy Decomposition (POTEC). It leverages clustering in the action space and learns two different policies via policy- and regression-based approaches, respectively. In particular, we derive a novel low-variance gradient estimator that enables to learn a first-stage policy for cluster selection efficiently via a policy-based approach. To select a specific action within the cluster sampled by the first-stage policy, POTEC uses a second-stage policy derived from a regression-based approach within each cluster. We show that a local correctness condition, which only requires that the regression model preserves the relative expected reward differences of the actions within each cluster, ensures that our policy-gradient estimator is unbiased and the second-stage policy is optimal. We also show that POTEC provides a strict generalization of policy- and regression-based approaches and their associated assumptions. Comprehensive experiments demonstrate that POTEC provides substantial improvements in OPL effectiveness particularly in large and structured action spaces.

The electronic map plays a crucial role in geographic information systems, serving various urban managerial scenarios and daily life services. Developing effective Map Entity Representation Learning (MERL) methods is crucial to extracting embedding information from electronic maps and converting map entities into representation vectors for downstream applications. However, existing MERL methods typically focus on one specific category of map entities, such as POIs, road segments, or land parcels, which is insufficient for real-world diverse map-based applications and might lose latent structural and semantic information interacting between entities of different types. Moreover, using representations generated by separate models for different map entities can introduce inconsistencies. Motivated by this, we propose a novel method named HOME-GCL for learning representations of multiple categories of map entities. Our approach utilizes a heterogeneous map entity graph (HOME graph) that integrates both road segments and land parcels into a unified framework. A HOME encoder with parcel-segment joint feature encoding and heterogeneous graph transformer is then deliberately designed to convert segments and parcels into representation vectors. Moreover, we introduce two types of contrastive learning tasks, namely intra-entity and inter-entity tasks, to train the encoder in a self-supervised manner. Extensive experiments on three large-scale datasets covering road segment-based, land parcel-based, and trajectory-based tasks demonstrate the superiority of our approach. To the best of our knowledge, HOME-GCL is the first attempt to jointly learn representations for road segments and land parcels using a unified model.

Visual SLAM (Simultaneous Localization and Mapping) based on planar features has found widespread applications in fields such as environmental structure perception and augmented reality. However, current research faces challenges in accurately localizing and mapping in planar ambiguous scenes, primarily due to the poor accuracy of the employed planar features and data association methods. In this paper, we propose a visual SLAM system based on planar features designed for planar ambiguous scenes, encompassing planar processing, data association, and multi-constraint factor graph optimization. We introduce a planar processing strategy that integrates semantic information with planar features, extracting the edges and vertices of planes to be utilized in tasks such as plane selection, data association, and pose optimization. Next, we present an integrated data association strategy that combines plane parameters, semantic information, projection IoU (Intersection over Union), and non-parametric tests, achieving accurate and robust plane data association in planar ambiguous scenes. Finally, we design a set of multi-constraint factor graphs for camera pose optimization. Qualitative and quantitative experiments conducted on publicly available datasets demonstrate that our proposed system competes effectively in both accuracy and robustness in terms of map construction and camera localization compared to state-of-the-art methods.