While the great capability of Transformers significantly boosts prediction accuracy, it could also yield overconfident predictions and require calibrated uncertainty estimation, which can be commonly tackled by Gaussian processes (GPs). Existing works apply GPs with symmetric kernels under variational inference to the attention kernel; however, omitting the fact that attention kernels are in essence asymmetric. Moreover, the complexity of deriving the GP posteriors remains high for large-scale data. In this work, we propose Kernel-Eigen Pair Sparse Variational Gaussian Processes (KEP-SVGP) for building uncertainty-aware self-attention where the asymmetry of attention kernels is tackled by Kernel SVD (KSVD) and a reduced complexity is acquired. Through KEP-SVGP, i) the SVGP pair induced by the two sets of singular vectors from KSVD w.r.t. the attention kernel fully characterizes the asymmetry; ii) using only a small set of adjoint eigenfunctions from KSVD, the derivation of SVGP posteriors can be based on the inversion of a diagonal matrix containing singular values, contributing to a reduction in time complexity; iii) an evidence lower bound is derived so that variational parameters can be optimized towards this objective. Experiments verify our excellent performances and efficiency on in-distribution, distribution-shift and out-of-distribution benchmarks.

In traditional Machine Learning, the algorithms predictions are based on the assumption that the data follows the same distribution in both the training and the test datasets. However, in real world data this condition does not hold and, for instance, the distribution of the covariates changes whereas the conditional distribution of the targets remains unchanged. This situation is called covariate shift problem where standard error estimation may be no longer accurate. In this context, the importance is a measure commonly used to alleviate the influence of covariate shift on error estimations. The main drawback is that it is not easy to compute. The Kullback-Leibler Importance Estimation Procedure (KLIEP) is capable of estimating importance in a promising way. Despite its good performance, it fails to ignore target information, since it only includes the covariates information for computing the importance. In this direction, this paper explores the potential performance improvement if target information is considered in the computation of the importance. Then, a redefinition of the importance arises in order to be generalized in this way. Besides the potential improvement in performance, including target information make possible the application to a real application about plankton classification that motivates this research and characterized by its great dimensionality, since considering targets rather than covariates reduces the computation and the noise in the covariates. The impact of taking target information is also explored when Logistic Regression (LR), Kernel Mean Matching (KMM), Ensemble Kernel Mean Matching (EKMM) and the naive predecessor of KLIEP called Kernel Density Estimation (KDE) methods estimate the importance. The experimental results lead to a more accurate error estimation using target information, especially in case of the more promising method KLIEP.

We study a general clustering setting in which we have $n$ elements to be clustered, and we aim to perform as few queries as possible to an oracle that returns a noisy sample of the similarity between two elements. Our setting encompasses many application domains in which the similarity function is costly to compute and inherently noisy. We propose two novel formulations of online learning problems rooted in the paradigm of Pure Exploration in Combinatorial Multi-Armed Bandits (PE-CMAB): fixed confidence and fixed budget settings. For both settings, we design algorithms that combine a sampling strategy with a classic approximation algorithm for correlation clustering and study their theoretical guarantees. Our results are the first examples of polynomial-time algorithms that work for the case of PE-CMAB in which the underlying offline optimization problem is NP-hard.

Self-supervised learning (SSL) learns representations by leveraging an auxiliary unsupervised task, such as classifying semantically related samples, e.g. different data augmentations or modalities. Of the many approaches to SSL, contrastive methods, e.g. SimCLR, CLIP and VicREG, have gained attention for learning representations that achieve downstream performance close to that of supervised learning. However, a theoretical understanding of the mechanism behind these methods eludes. We propose a generative latent variable model for the data and show that several families of discriminative self-supervised algorithms, including contrastive methods, approximately induce its latent structure over representations, providing a unifying theoretical framework. We also justify links to mutual information and the use of a projection head. Fitting our model generatively, as SimVE, improves performance over previous VAE methods on common benchmarks (e.g. FashionMNIST, CIFAR10, CelebA), narrows the gap to discriminative methods on _content_ classification and, as our analysis predicts, outperforms them where _style_ information is required, taking a step toward task-agnostic representations.

An important step in this direction It has repeatedly been observed that loss minimization by has been taken in Gurbuzbalaban et al. [2021], where the tail stochastic gradient descent leads to heavy-tailed distributions behavior of SGD iterates is characterized in dependence on of neural network parameters. Here, we analyze a continuous optimization parameters, dimension and Hessian curvature diffusion approximation of SGD, called homogenized stochastic at the loss minimum. One limitation of Gurbuzbalaban et al. gradient descent, show that it behaves asymptotically [2021] is that this link is described only qualitatively, but heavy-tailed, and give explicit upper and lower bounds on not quantitatively. Here, we provide an alternative approach its tail-index. We validate these bounds in numerical experiments through analyzing homogenized stochastic gradient descent, and show that they are typically close approximations a diffusion approximation of SGD introduced in Paquette to the empirical tail-index of SGD iterates.

In Hyperparameter Optimization (HPO), only the hyperparameter configuration with the best performance is chosen after performing several trials, then, discarding the effort of training all the models with every hyperparameter configuration trial and performing an ensemble of all them. This ensemble consists of simply averaging the model predictions or weighting the models by a certain probability. Recently, other more sophisticated ensemble strategies, such as the Caruana method or the stacking strategy has been proposed. On the one hand, the Caruana method performs well in HPO ensemble, since it is not affected by the effects of multicollinearity, which is prevalent in HPO. It just computes the average over a subset of predictions with replacement. But it does not benefit from the generalization power of a learning process. On the other hand, stacking methods include a learning procedure since a meta-learner is required to perform the ensemble. Yet, one hardly finds advice about which meta-learner is adequate. Besides, some meta-learners may suffer from the effects of multicollinearity or need to be tuned to reduce them. This paper explores meta-learners for stacking ensemble in HPO, free of hyperparameter tuning, able to reduce the effects of multicollinearity and considering the ensemble learning process generalization power. At this respect, the boosting strategy seems promising as a stacking meta-learner. In fact, it completely removes the effects of multicollinearity. This paper also proposes an implicit regularization in the classical boosting method and a novel non-parametric stop criterion suitable only for boosting and specifically designed for HPO. The synergy between these two improvements over boosting exhibits competitive and promising predictive power performance compared to other existing meta-learners and ensemble approaches for HPO other than the stacking ensemble.

Machine learning (ML) plays a pivotal role in detecting malicious software. Despite the high F1-scores reported in numerous studies reaching upwards of 0.99, the issue is not completely solved. Malware detectors often experience performance decay due to constantly evolving operating systems and attack methods, which can render previously learned knowledge insufficient for accurate decision-making on new inputs. This paper argues that commonly reported results are inflated due to two pervasive sources of experimental bias in the detection task: spatial bias caused by data distributions that are not representative of a real-world deployment; and temporal bias caused by incorrect time splits of data, leading to unrealistic configurations. To address these biases, we introduce a set of constraints for fair experiment design, and propose a new metric, AUT, for classifier robustness in real-world settings. We additionally propose an algorithm designed to tune training data to enhance classifier performance. Finally, we present TESSERACT, an open-source framework for realistic classifier comparison. Our evaluation encompasses both traditional ML and deep learning methods, examining published works on an extensive Android dataset with 259,230 samples over a five-year span. Additionally, we conduct case studies in the Windows PE and PDF domains. Our findings identify the existence of biases in previous studies and reveal that significant performance enhancements are possible through appropriate, periodic tuning. We explore how mitigation strategies may support in achieving a more stable and better performance over time by employing multiple strategies to delay performance decay.

There is an intricate relation between the properties of an image and how humans behave while describing the image. This behavior shows ample variation, as manifested in human signals such as eye movements and when humans start to describe the image. Despite the value of such signals of visuo-linguistic variation, they are virtually disregarded in the training of current pretrained models, which motivates further investigation. Using a corpus of Dutch image descriptions with concurrently collected eye-tracking data, we explore the nature of the variation in visuo-linguistic signals, and find that they correlate with each other. Given this result, we hypothesize that variation stems partly from the properties of the images, and explore whether image representations encoded by pretrained vision encoders can capture such variation. Our results indicate that pretrained models do so to a weak-to-moderate degree, suggesting that the models lack biases about what makes a stimulus complex for humans and what leads to variations in human outputs.

We develop a family of distributed clustering algorithms that work over networks of users. In the proposed scenario, users contain a local dataset and communicate only with their immediate neighbours, with the aim of finding a clustering of the full, joint data. The proposed family, termed Distributed Gradient Clustering (DGC-$\mathcal{F}_\rho$), is parametrized by $\rho \geq 1$, controling the proximity of users' center estimates, with $\mathcal{F}$ determining the clustering loss. Specialized to popular clustering losses like $K$-means and Huber loss, DGC-$\mathcal{F}_\rho$ gives rise to novel distributed clustering algorithms DGC-KM$_\rho$ and DGC-HL$_\rho$, while a novel clustering loss based on the logistic function leads to DGC-LL$_\rho$. We provide a unified analysis and establish several strong results, under mild assumptions. First, the sequence of centers generated by the methods converges to a well-defined notion of fixed point, under any center initialization and value of $\rho$. Second, as $\rho$ increases, the family of fixed points produced by DGC-$\mathcal{F}_\rho$ converges to a notion of consensus fixed points. We show that consensus fixed points of DGC-$\mathcal{F}_{\rho}$ are equivalent to fixed points of gradient clustering over the full data, guaranteeing a clustering of the full data is produced. For the special case of Bregman losses, we show that our fixed points converge to the set of Lloyd points. Numerical experiments on real data confirm our theoretical findings and demonstrate strong performance of the methods.

Large language models based on the Transformer architecture have demonstrated impressive capabilities to learn in context. However, existing theoretical studies on how this phenomenon arises are limited to the dynamics of a single layer of attention trained on linear regression tasks. In this paper, we study the optimization of a Transformer consisting of a fully connected layer followed by a linear attention layer. The MLP acts as a common nonlinear representation or feature map, greatly enhancing the power of in-context learning. We prove in the mean-field and two-timescale limit that the infinite-dimensional loss landscape for the distribution of parameters, while highly nonconvex, becomes quite benign. We also analyze the second-order stability of mean-field dynamics and show that Wasserstein gradient flow almost always avoids saddle points. Furthermore, we establish novel methods for obtaining concrete improvement rates both away from and near critical points. This represents the first saddle point analysis of mean-field dynamics in general and the techniques are of independent interest.