In this paper, we propose a new class of positive definite kernels based on the spectral truncation, which has been discussed in the fields of noncommutative geometry and $C^*$-algebra. We focus on kernels whose inputs and outputs are functions and generalize existing kernels, such as polynomial, product, and separable kernels, by introducing a truncation parameter $n$ that describes the noncommutativity of the products appearing in the kernels. When $n$ goes to infinity, the proposed kernels tend to the existing commutative kernels. If $n$ is finite, they exhibit different behavior, and the noncommutativity induces interactions along the data function domain. We show that the truncation parameter $n$ is a governing factor leading to performance enhancement: by setting an appropriate $n$, we can balance the representation power and the complexity of the representation space. The flexibility of the proposed class of kernels allows us to go beyond previous commutative kernels.

Decentralized machine learning approaches are increasingly popular in numerous applications such as the internet-of-things (IoT) and networked autonomous systems [Marvasti et al., 2014, Savazzi et al., 2020], primarily due to their scalability to larger datasets and systems, as well as their respect for data locality and privacy concerns. In this work, we focus on decentralized optimization techniques that operate without a central coordinator, relying solely on on-device computation and local communication with neighboring devices. This encompasses traditional scenarios like training Machine Learning models in large data centers, as well as emerging applications where computations occur directly on devices. Such a setting is preferred over centralized topology which often poses a significant bottleneck on the central node in terms of communication latency, bandwidth, and fault tolerance. Considering the enormous size of modern Machine Learning models, classic single-node training is often impossible. Moreover, the training of large models requires a huge amount of data that does not fit the memory of a single machine. Therefore, modern training techniques heavily rely on distributed computations over a set of computation nodes/clients [Shoeybi et al., 2019, Wang et al., 2020, Ramesh et al., 2021, 2022]. One of the instances of distributed training is Federated Learning (FL) [Konecnỳ et al., 2016, Kairouz et al., 2021] which has recently gathered a lot of attention.

Predictive posterior densities (PPDs) are of interest in approximate Bayesian inference. Typically, these are estimated by simple Monte Carlo (MC) averages using samples from the approximate posterior. We observe that the signal-to-noise ratio (SNR) of such estimators can be extremely low. An analysis for exact inference reveals SNR decays exponentially as there is an increase in (a) the mismatch between training and test data, (b) the dimensionality of the latent space, or (c) the size of the test data relative to the training data. Further analysis extends these results to approximate inference. To remedy the low SNR problem, we propose replacing simple MC sampling with importance sampling using a proposal distribution optimized at test time on a variational proxy for the SNR and demonstrate that this yields greatly improved estimates.

Label noise, commonly found in real-world datasets, has a detrimental impact on a model's generalization. To effectively detect incorrectly labeled instances, previous works have mostly relied on distinguishable training signals, such as training loss, as indicators to differentiate between clean and noisy labels. However, they have limitations in that the training signals incompletely reveal the model's behavior and are not effectively generalized to various noise types, resulting in limited detection accuracy. In this paper, we propose DynaCor framework that distinguishes incorrectly labeled instances from correctly labeled ones based on the dynamics of the training signals. To cope with the absence of supervision for clean and noisy labels, DynaCor first introduces a label corruption strategy that augments the original dataset with intentionally corrupted labels, enabling indirect simulation of the model's behavior on noisy labels. Then, DynaCor learns to identify clean and noisy instances by inducing two clearly distinguishable clusters from the latent representations of training dynamics. Our comprehensive experiments show that DynaCor outperforms the state-of-the-art competitors and shows strong robustness to various noise types and noise rates.

The 2024 Index is our most comprehensive to date and arrives at an important moment when AI's influence on society has never been more pronounced. This year, we have broadened our scope to more extensively cover essential trends such as technical advancements in AI, public perceptions of the technology, and the geopolitical dynamics surrounding its development. Featuring more original data than ever before, this edition introduces new estimates on AI training costs, detailed analyses of the responsible AI landscape, and an entirely new chapter dedicated to AI's impact on science and medicine. The AI Index report tracks, collates, distills, and visualizes data related to artificial intelligence (AI). Our mission is to provide unbiased, rigorously vetted, broadly sourced data in order for policymakers, researchers, executives, journalists, and the general public to develop a more thorough and nuanced understanding of the complex field of AI. The AI Index is recognized globally as one of the most credible and authoritative sources for data and insights on artificial intelligence. Previous editions have been cited in major newspapers, including the The New York Times, Bloomberg, and The Guardian, have amassed hundreds of academic citations, and been referenced by high-level policymakers in the United States, the United Kingdom, and the European Union, among other places. This year's edition surpasses all previous ones in size, scale, and scope, reflecting the growing significance that AI is coming to hold in all of our lives.

Despite their benefits in terms of simplicity, low computational cost and data requirement, parametric machine learning algorithms, such as linear discriminant analysis, quadratic discriminant analysis or logistic regression, suffer from serious drawbacks including linearity, poor fit of features to the usually imposed normal distribution and high dimensionality. Batch kernel-based nonparametric classifier, which overcomes the linearity and normality of features constraints, represent an interesting alternative for supervised classification problem. However, it suffers from the ``curse of dimension". The problem can be alleviated by the explosive sample size in the era of big data, while large-scale data size presents some challenges in the storage of data and the calculation of the classifier. These challenges make the classical batch nonparametric classifier no longer applicable. This motivates us to develop a fast algorithm adapted to the real-time calculation of the nonparametric classifier in massive as well as streaming data frameworks. This online classifier includes two steps. First, we consider an online principle components analysis to reduce the dimension of the features with a very low computation cost. Then, a stochastic approximation algorithm is deployed to obtain a real-time calculation of the nonparametric classifier. The proposed methods are evaluated and compared to some commonly used machine learning algorithms for real-time fetal well-being monitoring. The study revealed that, in terms of accuracy, the offline (or Batch), as well as, the online classifiers are good competitors to the random forest algorithm. Moreover, we show that the online classifier gives the best trade-off accuracy/computation cost compared to the offline classifier.

Alzheimer's Disease (AD) is a progressive neurodegenerative disorder that primarily affects the aging population by impairing cognitive and motor functions. Early detection of AD through accessible methodologies like magnetic resonance imaging (MRI) is vital for developing effective interventions to halt or slow the disease's progression. This study aims to perform a comprehensive analysis of machine learning techniques for selecting MRI-based biomarkers and classifying individuals into healthy controls (HC) and unstable controls (uHC) who later show mild cognitive impairment within five years. The research utilizes MRI data from the Alzheimer's Disease Neuroinformatics Initiative (ADNI) and the Open Access Series of Imaging Studies 3 (OASIS-3), focusing on both HC and uHC participants. The study addresses the challenges of imbalanced data by testing classification methods on balanced and unbalanced datasets, and harmonizes data using polynomial regression to mitigate nuisance variables like age, gender, and intracranial volume. Results indicate that Gaussian Naive Bayes and RusBoost classifiers shows an optimal performance, achieving accuracies of up to 76.46% and 72.48% respectively on the ADNI dataset. For the OASIS-3 dataset, Kernel Naive Bayes and RusBoost yield accuracies ranging from 64.66% to 75.71%, improving further in age-matched datasets. Brain regions like the entorhinal cortex, hippocampus, lateral ventricle, and lateral orbitofrontal cortex are identified as significantly impacted during early cognitive decline. Despite limitations such as small sample sizes, the study's harmonization approach enhances the robustness of biomarker selection, suggesting the potential of this semi-automatic machine learning pipeline for early AD detection using MRI.

Student data, which is a critical component in EDM research, can contain personal information, such as age and gender, as well as academic performance and activity data from online learning systems [24]. By offering valuable insights into student learning, EDM supports the development of more effective educational practices and policies, ultimately improving student outcomes. One of the most popular techniques in the previous works is incorporating machine learning techniques, which has achieved remarkable success in discovering intricate structures within educational datasets. However, in recent years, concerns about the fairness of deploying algorithmic decision-making in the educational context have emerged [2, 22, 27, 49]. Particularly, machine learning models can produce biased and unfair outcomes for certain student groups, significantly affecting their educational opportunities and achievements. Given that the data empowering EDM research can often contain personally identifiable and other sensitive information, there has been increased attention to privacy protection in recent years [37, 43]. Additionally, privacy legislation such as the California Consumer Privacy Act [39] and the former Right to be Forgotten [17] has granted users the right to erase the impact of their sensitive information from the trained models to protect their privacy. One approach to protecting users' privacy involves enabling the trained machine learning model to entirely forget Both authors contributed equally to this research.

Humans rely on strong inductive biases to learn from few examples and abstract useful information from sensory data. Instilling such biases in machine learning models has been shown to improve their performance on various benchmarks including few-shot learning, robustness, and alignment. However, finding effective training procedures to achieve that goal can be challenging as psychologically-rich training data such as human similarity judgments are expensive to scale, and Bayesian models of human inductive biases are often intractable for complex, realistic domains. Here, we address this challenge by introducing a Bayesian notion of generative similarity whereby two datapoints are considered similar if they are likely to have been sampled from the same distribution. This measure can be applied to complex generative processes, including probabilistic programs. We show that generative similarity can be used to define a contrastive learning objective even when its exact form is intractable, enabling learning of spatial embeddings that express specific inductive biases. We demonstrate the utility of our approach by showing how it can be used to capture human inductive biases for geometric shapes, and to better distinguish different abstract drawing styles that are parameterized by probabilistic programs.

We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics. SMC is a Markov Chain Monte Carlo (MCMC) method, which starts by drawing $N$ particles from a known distribution, and then, through a sequence of distributions, re-weights and re-samples the particles, at each instance applying a Markov chain for smoothing. In principle, SMC tries to alleviate problems from multi-modality. However, most theoretical guarantees for SMC are obtained by assuming global mixing time bounds, which are only efficient in the uni-modal setting. We show that bounds can be obtained in the truly multi-modal setting, with mixing times that depend only on local MCMC dynamics.