Deep networks are prone to performance degradation To carry out this adaptation, a range of methods with varying when there is a domain shift between the requirements on the availability of source and target domain source (training) data and target (test) data. Recent data have been developed. In the classic domain adaptation test-time adaptation methods update batch normalization (DA) setting, methods assume source and target data are layers of pre-trained source models deployed jointly available for training [Wilson and Cook, 2020], which in new target environments with streaming compromises the privacy of source domain data. To address data to mitigate such performance degradation. Although this, methods for the source-free DA setting [Qiu et al., 2021; such methods can adapt on-the-fly without Yang et al., 2021; Liang et al., 2020] instead adapt a pretrained first collecting a large target domain dataset, source model using only unlabeled target data, but their performance is dependent on streaming conditions they still require access to the entire unlabeled target dataset such as mini-batch size and class-distribution, like traditional DA methods. This can delay adaptation, or which can be unpredictable in practice. In this even make it impractical, when collecting the unlabeled target work, we propose a framework for few-shot domain data is costly in terms of time or other resources.

The matrix completion problem seeks to recover a $d\times d$ ground truth matrix of low rank $r\ll d$ from observations of its individual elements. Real-world matrix completion is often a huge-scale optimization problem, with $d$ so large that even the simplest full-dimension vector operations with $O(d)$ time complexity become prohibitively expensive. Stochastic gradient descent (SGD) is one of the few algorithms capable of solving matrix completion on a huge scale, and can also naturally handle streaming data over an evolving ground truth. Unfortunately, SGD experiences a dramatic slow-down when the underlying ground truth is ill-conditioned; it requires at least $O(\kappa\log(1/\epsilon))$ iterations to get $\epsilon$-close to ground truth matrix with condition number $\kappa$. In this paper, we propose a preconditioned version of SGD that preserves all the favorable practical qualities of SGD for huge-scale online optimization while also making it agnostic to $\kappa$. For a symmetric ground truth and the Root Mean Square Error (RMSE) loss, we prove that the preconditioned SGD converges to $\epsilon$-accuracy in $O(\log(1/\epsilon))$ iterations, with a rapid linear convergence rate as if the ground truth were perfectly conditioned with $\kappa=1$. In our experiments, we observe a similar acceleration for item-item collaborative filtering on the MovieLens25M dataset via a pair-wise ranking loss, with 100 million training pairs and 10 million testing pairs. [See supporting code at https://github.com/Hong-Ming/ScaledSGD.]

High-Dimensional and Incomplete (HDI) data are frequently found in various industrial applications with complex interactions among numerous nodes, which are commonly non-negative for representing the inherent non-negativity of node interactions. A Non-negative Latent Factor (NLF) model is able to extract intrinsic features from such data efficiently. However, existing NLF models all adopt a static divergence metric like Euclidean distance or {\alpha}-\b{eta} divergence to build its learning objective, which greatly restricts its scalability of accurately representing HDI data from different domains. Aiming at addressing this issue, this study presents an Adaptive Divergence-based Non-negative Latent Factor (ADNLF) model with three-fold ideas: a) generalizing the objective function with the {\alpha}-\b{eta}-divergence to expand its potential of representing various HDI data; b) adopting a non-negative bridging function to connect the optimization variables with output latent factors for fulfilling the non-negativity constraints constantly; and c) making the divergence parameters adaptive through particle swarm optimization, thereby facilitating adaptive divergence in the learning objective to achieve high scalability. Empirical studies are conducted on four HDI datasets from real applications, whose results demonstrate that in comparison with state-of-the-art NLF models, an ADNLF model achieves significantly higher estimation accuracy for missing data of an HDI dataset with high computational efficiency.

Prompt Tuning has been largely successful as a parameter-efficient method of conditioning large-scale pre-trained language models to perform downstream tasks. Thus far, soft prompt tuning learns a fixed set of task-specific continuous vectors, i.e., soft tokens that remain static across the task samples. A fixed prompt, however, may not generalize well to the diverse kinds of inputs the task comprises. In order to address this, we propose Vector-quantized Input-contextualized Prompts (VIP) as an extension to the soft prompt tuning framework. VIP particularly focuses on two aspects -- contextual prompts that learns input-specific contextualization of the soft prompt tokens through a small-scale sentence encoder and quantized prompts that maps the contextualized prompts to a set of learnable codebook vectors through a Vector quantization network. On various language understanding tasks like SuperGLUE, QA, Relation classification, NER and NLI, VIP outperforms the soft prompt tuning (PT) baseline by an average margin of 1.19%. Further, our generalization studies show that VIP learns more robust prompt representations, surpassing PT by a margin of 0.6% - 5.3% on Out-of-domain QA and NLI tasks respectively, and by 0.75% on Multi-Task setup over 4 tasks spanning across 12 domains.

We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.

Modern machine learning architectures are often highly expressive. They are usually over-parameterized and can interpolate the data by driving the empirical loss close to zero. We analyze the convergence of Local SGD (or FedAvg) for such over-parameterized models in the heterogeneous data setting and improve upon the existing literature by establishing the following convergence rates. We show an error bound of $\O(\exp(-T))$ for strongly-convex loss functions, where $T$ is the total number of iterations. For general convex loss functions, we establish an error bound of $\O(1/T)$ under a mild data similarity assumption and an error bound of $\O(K/T)$ otherwise, where $K$ is the number of local steps. We also extend our results for non-convex loss functions by proving an error bound of $\O(K/T)$. Before our work, the best-known convergence rate for strongly-convex loss functions was $\O(\exp(-T/K))$, and none existed for general convex or non-convex loss functions under the overparameterized setting. We complete our results by providing problem instances in which such convergence rates are tight to a constant factor under a reasonably small stepsize scheme. Finally, we validate our theoretical results using numerical experiments on real and synthetic data.

Contemporary vision benchmarks predominantly consider tasks on which humans can achieve near-perfect performance. However, humans are frequently presented with visual data that they cannot classify with 100% certainty, and models trained on standard vision benchmarks achieve low performance when evaluated on this data. To address this issue, we introduce a procedure for creating datasets of ambiguous images and use it to produce SQUID-E ("Squidy"), a collection of noisy images extracted from videos. All images are annotated with ground truth values and a test set is annotated with human uncertainty judgments. We use this dataset to characterize human uncertainty in vision tasks and evaluate existing visual event classification models. Experimental results suggest that existing vision models are not sufficiently equipped to provide meaningful outputs for ambiguous images and that datasets of this nature can be used to assess and improve such models through model training and direct evaluation of model calibration. These findings motivate large-scale ambiguous dataset creation and further research focusing on noisy visual data.

Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.

By Vincent Granville Ph.D. Published in September 2022. This book covers the foundations of machine learning, with modern approaches to solving complex problems. Emphasis is on scalability, automation, testing, optimizing, and interpretability (explainable AI). For instance, regression techniques -- including logistic and Lasso -- are presented as a single method, without using advanced linear algebra. There is no need to learn 50 versions when one does it all and more.

Abstract: A novel family of geometric signal detectors are proposed through medians of the total Bregman divergence (TBD), which are shown advantageous over the conventional methods and their mean counterparts. As is difficult to be solved analytically, we propose numerical solutions through Riemannian gradient descent algorithms or fixed-point algorithms. Beside detection performance, robustness of a detector to outliers is also of vital importance, which can often be analyzed via the influence functions. Introducing an orthogonal basis for Hermitian matrices, we are able to compute the corresponding influence functions analytically and exactly by solving a linear system, which is transformed from the governing matrix equation. Numerical simulations show that the TBD medians are more robust than their mean counterparts.