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 Statistical Learning


AlbNews: A Corpus of Headlines for Topic Modeling in Albanian

arXiv.org Artificial Intelligence

The scarcity of available text corpora for low-resource languages like Albanian is a serious hurdle for research in natural language processing tasks. This paper introduces AlbNews, a collection of 600 topically labeled news headlines and 2600 unlabeled ones in Albanian. The data can be freely used for conducting topic modeling research. We report the initial classification scores of some traditional machine learning classifiers trained with the AlbNews samples. These results show that basic models outrun the ensemble learning ones and can serve as a baseline for future experiments.


Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimisation

arXiv.org Artificial Intelligence

We study the effect of the batch size to the total gradient variance in differentially private stochastic gradient descent (DP-SGD), seeking a theoretical explanation for the usefulness of large batch sizes. As DP-SGD is the basis of modern DP deep learning, its properties have been widely studied, and recent works have empirically found large batch sizes to be beneficial. However, theoretical explanations of this benefit are currently heuristic at best. We first observe that the total gradient variance in DP-SGD can be decomposed into subsampling-induced and noise-induced variances. We then prove that in the limit of an infinite number of iterations, the effective noise-induced variance is invariant to the batch size. The remaining subsampling-induced variance decreases with larger batch sizes, so large batches reduce the effective total gradient variance. We confirm numerically that the asymptotic regime is relevant in practical settings when the batch size is not small, and find that outside the asymptotic regime, the total gradient variance decreases even more with large batch sizes. We also find a sufficient condition that implies that large batch sizes similarly reduce effective DP noise variance for one iteration of DP-SGD.


A Bias-Variance Decomposition for Ensembles over Multiple Synthetic Datasets

arXiv.org Artificial Intelligence

Recent studies have highlighted the benefits of generating multiple synthetic datasets for supervised learning, from increased accuracy to more effective model selection and uncertainty estimation. These benefits have clear empirical support, but the theoretical understanding of them is currently very light. We seek to increase the theoretical understanding by deriving bias-variance decompositions for several settings of using multiple synthetic datasets. Our theory predicts multiple synthetic datasets to be especially beneficial for high-variance downstream predictors, and yields a simple rule of thumb to select the appropriate number of synthetic datasets in the case of mean-squared error and Brier score. We investigate how our theory works in practice by evaluating the performance of an ensemble over many synthetic datasets for several real datasets and downstream predictors. The results follow our theory, showing that our insights are also practically relevant.


On Convergence of Adam for Stochastic Optimization under Relaxed Assumptions

arXiv.org Artificial Intelligence

The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex smooth scenarios with potential unbounded gradients and affine variance noise. In this paper, we study vanilla Adam under these challenging conditions. We introduce a comprehensive noise model which governs affine variance noise, bounded noise and sub-Gaussian noise. We show that Adam can find a stationary point with a $\mathcal{O}(\text{poly}(\log T)/\sqrt{T})$ rate in high probability under this general noise model where $T$ denotes total number iterations, matching the lower rate of stochastic first-order algorithms up to logarithm factors. More importantly, we reveal that Adam is free of tuning step-sizes with any problem-parameters, yielding a better adaptation property than the Stochastic Gradient Descent under the same conditions. We also provide a probabilistic convergence result for Adam under a generalized smooth condition which allows unbounded smoothness parameters and has been illustrated empirically to more accurately capture the smooth property of many practical objective functions.


On dimensionality of feature vectors in MPNNs

arXiv.org Artificial Intelligence

We revisit the classical result of Morris et al.~(AAAI'19) that message-passing graphs neural networks (MPNNs) are equal in their distinguishing power to the Weisfeiler--Leman (WL) isomorphism test. Morris et al.~show their simulation result with ReLU activation function and $O(n)$-dimensional feature vectors, where $n$ is the number of nodes of the graph. Recently, by introducing randomness into the architecture, Aamand et al.~(NeurIPS'22) were able to improve this bound to $O(\log n)$-dimensional feature vectors, although at the expense of guaranteeing perfect simulation only with high probability. In all these constructions, to guarantee equivalence to the WL test, the dimension of feature vectors in the MPNN has to increase with the size of the graphs. However, architectures used in practice have feature vectors of constant dimension. Thus, there is a gap between the guarantees provided by these results and the actual characteristics of architectures used in practice. In this paper we close this gap by showing that, for \emph{any} non-polynomial analytic (like the sigmoid) activation function, to guarantee that MPNNs are equivalent to the WL test, feature vectors of dimension $d=1$ is all we need, independently of the size of the graphs. Our main technical insight is that for simulating multi-sets in the WL-test, it is enough to use linear independence of feature vectors over rationals instead of reals. Countability of the set of rationals together with nice properties of analytic functions allow us to carry out the simulation invariant over the iterations of the WL test without increasing the dimension of the feature vectors.


Approximating the Core via Iterative Coalition Sampling

arXiv.org Artificial Intelligence

The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, and to fully embrace cooperative game theory contributions in domains such as explainable AI (XAI), where the core can complement the Shapley values to identify influential features or instances supporting predictions by black-box models. We propose novel iterative algorithms for computing variants of the core, which avoid the computational bottleneck of many other approaches; namely solving large linear programs. As such, they scale better to very large problems as we demonstrate across different classes of cooperative games, including weighted voting games, induced subgraph games, and marginal contribution networks. We also explore our algorithms in the context of XAI, providing further evidence of the power of the core for such applications.


Elastic Feature Consolidation for Cold Start Exemplar-free Incremental Learning

arXiv.org Artificial Intelligence

Exemplar-Free Class Incremental Learning (EFCIL) aims to learn from a sequence of tasks without having access to previous task data. In this paper, we consider the challenging Cold Start scenario in which insufficient data is available in the first task to learn a high-quality backbone. This is especially challenging for EFCIL since it requires high plasticity, which results in feature drift which is difficult to compensate for in the exemplar-free setting. To address this problem, we propose a simple and effective approach that consolidates feature representations by regularizing drift in directions highly relevant to previous tasks and employs prototypes to reduce task-recency bias. Our method, called Elastic Feature Consolidation (EFC), exploits a tractable second-order approximation of feature drift based on an Empirical Feature Matrix (EFM). The EFM induces a pseudo-metric in feature space which we use to regularize feature drift in important directions and to update Gaussian prototypes used in a novel asymmetric cross entropy loss which effectively balances prototype rehearsal with data from new tasks. Experimental results on CIFAR-100, Tiny-ImageNet, ImageNet-Subset and ImageNet-1K demonstrate that Elastic Feature Consolidation is better able to learn new tasks by maintaining model plasticity and significantly outperform the state-of-the-art. Deep neural networks achieve state-of-the-art performance on a broad range of visual recognition problems. However, the traditional supervised learning paradigm is limited in that it presumes all training data for all tasks is available in a single training session. The goal of Class-Incremental Learning (CIL) is to enable incremental integration of new classification tasks into already-trained models as they become available (Masana et al., 2022). Class-incremental learning entails balancing model plasticity (to allow learning of new tasks) against model stability (to avoid catastrophic forgetting of previous tasks) (McCloskey & Cohen, 1989). Exemplar-based approaches retain a small set of samples from previous tasks which are replayed to avoid forgetting, while exemplar-free methods retain no samples from previous tasks.


Employee Turnover Analysis Using Machine Learning Algorithms

arXiv.org Artificial Intelligence

Employee's knowledge is an organization asset. Turnover may impose apparent and hidden costs and irreparable damages. To overcome and mitigate this risk, employee's condition should be monitored. Due to high complexity of analyzing well-being features, employee's turnover predicting can be delegated to machine learning techniques. In this paper, we discuss employee's attrition rate. Three different supervised learning algorithms comprising AdaBoost, SVM and RandomForest are used to benchmark employee attrition accuracy. Attained models can help out at establishing predictive analytics.


A phase transition between positional and semantic learning in a solvable model of dot-product attention

arXiv.org Artificial Intelligence

We investigate how a dot-product attention layer learns a positional attention matrix (with tokens attending to each other based on their respective positions) and a semantic attention matrix (with tokens attending to each other based on their meaning). For an algorithmic task, we experimentally show how the same simple architecture can learn to implement a solution using either the positional or semantic mechanism. On the theoretical side, we study the learning of a non-linear self-attention layer with trainable tied and low-rank query and key matrices. In the asymptotic limit of high-dimensional data and a comparably large number of training samples, we provide a closed-form characterization of the global minimum of the non-convex empirical loss landscape. We show that this minimum corresponds to either a positional or a semantic mechanism and evidence an emergent phase transition from the former to the latter with increasing sample complexity. Finally, we compare the dot-product attention layer to linear positional baseline, and show that it outperforms the latter using the semantic mechanism provided it has access to sufficient data.


MOMENT: A Family of Open Time-series Foundation Models

arXiv.org Artificial Intelligence

Time-series analysis is an important field encompassing a wide range of applications ranging from forecasting weather patterns Schneider and Dickinson [1974] or detecting irregular heartbeats using Electrocardiograms Goswami et al. [2021], to identifying anomalous software deployments Xu et al. [2018]. Due to its significant practical value and the unique challenges that modeling time-series data poses, time-series analysis continues to receive substantial interest from academia and industry alike. However, modeling such data typically requires substantial domain expertise, time, and task-specific design. Large pre-trained language Touvron et al. [2023], Devlin et al. [2019], Chung et al. [2022], vision Li et al. [2023a], and video Day et al. [2023] models, typically perform well on a variety of tasks on data from diverse domains, with little or no supervision, and they can be specialized to perform well on specific tasks. We unlock these key capabilities for time-series data and release the first family of open-source large pre-trained time-series models, which we call MOMENT. The models in this family (1) serve as a building block for diverse time-series analysis tasks (e.g., forecasting, classification, anomaly detection, and imputation, etc.), (2) are effective out-of-the-box, i.e., with no (or few) particular task-specific exemplars (enabling e.g., zero-shot forecasting, few-shot classification, etc.), and (3) are tunable using in-distribution and task-specific data to improve performance. MOMENT is a family of high-capacity transformer models, pre-trained using a masked time-series prediction task on large amounts of time-series data drawn from diverse domains. Below we summarize our key contributions.