Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned quantum machine learning (QML) as a potential source of such useful exponential improvements. Yet, in an unexpected development, a recent series of "dequantization" results has equally rapidly removed the promise of exponential speedups for several QML algorithms. This raises the critical question whether exponential speedups of other linear-algebraic QML algorithms persist. In this paper, we study the quantum-algorithmic methods behind the algorithm for topological data analysis of Lloyd, Garnerone and Zanardi through this lens. We provide evidence that the problem solved by this algorithm is classically intractable by showing that its natural generalization is as hard as simulating the one clean qubit model -- which is widely believed to require superpolynomial time on a classical computer -- and is thus very likely immune to dequantizations. Based on this result, we provide a number of new quantum algorithms for problems such as rank estimation and complex network analysis, along with complexity-theoretic evidence for their classical intractability. Furthermore, we analyze the suitability of the proposed quantum algorithms for near-term implementations. Our results provide a number of useful applications for full-blown, and restricted quantum computers with a guaranteed exponential speedup over classical methods, recovering some of the potential for linear-algebraic QML to become one of quantum computing's killer applications.

To ensure reliability, power transformers are monitored for partial discharge (PD) events, which are symptoms of transformer failure. Since failures can have catastrophic cascading consequences, it is critical to preempt them as early as possible. Our goal is to classify PDs as corona, floating, particle, or void, to gain an understanding of the failure location. Using phase resolved PD signal data, we create a small set of features, which can be used to classify PDs with high accuracy. This set of features consists of the total magnitude, the maximum magnitude, and the length of the longest empty band. These features represent the entire signal and not just a single phase, so the feature set has a fixed size and is easily comprehensible. With both Random Forest and SVM classification methods, we attain a 99% classification accuracy, which is significantly higher than classification using phase based feature sets such as phase magnitude. Furthermore, we develop a stacking ensemble to combine several classification models, resulting in a superior model that outperforms existing methods in both accuracy and variance.

We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss $\ell$ can control the test error under all Moreau envelopes of the loss $\ell$. We use our finite-sample bound to directly recover the "optimistic rate" of Zhou et al. (2021) for linear regression with the square loss, which is known to be tight for minimal $\ell_2$-norm interpolation, but we also handle more general settings where the label is generated by a potentially misspecified multi-index model. The same argument can analyze noisy interpolation of max-margin classifiers through the squared hinge loss, and establishes consistency results in spiked-covariance settings. More generally, when the loss is only assumed to be Lipschitz, our bound effectively improves Talagrand's well-known contraction lemma by a factor of two, and we prove uniform convergence of interpolators (Koehler et al. 2021) for all smooth, non-negative losses. Finally, we show that application of our generalization bound using localized Gaussian width will generally be sharp for empirical risk minimizers, establishing a non-asymptotic Moreau envelope theory for generalization that applies outside of proportional scaling regimes, handles model misspecification, and complements existing asymptotic Moreau envelope theories for M-estimation.

One common approach to detecting change-points is minimizing a cost function over possible numbers and locations of change-points. The framework includes several well-established procedures, such as the penalized likelihood and minimum description length. Such an approach requires finding the cost value repeatedly over different segments of the data set, which can be time-consuming when (i) the data sequence is long and (ii) obtaining the cost value involves solving a non-trivial optimization problem. This paper introduces a new sequential method (SE) that can be coupled with gradient descent (SeGD) and quasi-Newton's method (SeN) to find the cost value effectively. The core idea is to update the cost value using the information from previous steps without re-optimizing the objective function. The new method is applied to change-point detection in generalized linear models and penalized regression. Numerical studies show that the new approach can be orders of magnitude faster than the Pruned Exact Linear Time (PELT) method without sacrificing estimation accuracy.

A fundamental task in science is to design experiments that yield valuable insights about the system under study. Mathematically, these insights can be represented as a utility or risk function that shapes the value of conducting each experiment. We present PDBAL, a targeted active learning method that adaptively designs experiments to maximize scientific utility. PDBAL takes a user-specified risk function and combines it with a probabilistic model of the experimental outcomes to choose designs that rapidly converge on a high-utility model. We prove theoretical bounds on the label complexity of PDBAL and provide fast closed-form solutions for designing experiments with common exponential family likelihoods. In simulation studies, PDBAL consistently outperforms standard untargeted approaches that focus on maximizing expected information gain over the design space. Finally, we demonstrate the scientific potential of PDBAL through a study on a large cancer drug screen dataset where PDBAL quickly recovers the most efficacious drugs with a small fraction of the total number of experiments.

Code search, which aims at retrieving the most relevant code fragment for a given natural language query, is a common activity in software development practice. Recently, contrastive learning is widely used in code search research, where many data augmentation approaches for source code (e.g., semantic-preserving program transformation) are proposed to learn better representations. However, these augmentations are at the raw-data level, which requires additional code analysis in the preprocessing stage and additional training costs in the training stage. In this paper, we explore augmentation methods that augment data (both code and query) at representation level which does not require additional data processing and training, and based on this we propose a general format of representation-level augmentation that unifies existing methods. Then, we propose three new augmentation methods (linear extrapolation, binary interpolation, and Gaussian scaling) based on the general format. Furthermore, we theoretically analyze the advantages of the proposed augmentation methods over traditional contrastive learning methods on code search. We experimentally evaluate the proposed representation-level augmentation methods with state-of-the-art code search models on a large-scale public dataset consisting of six programming languages. The experimental results show that our approach can consistently boost the performance of the studied code search models. Our source code is available at https://github.com/Alex-HaochenLi/RACS.

We seek to semantically describe a set of images, capturing both the attributes of single images and the variations within the set. Our procedure is analogous to Principle Component Analysis, in which the role of projection vectors is replaced with generated phrases. First, a centroid phrase that has the largest average semantic similarity to the images in the set is generated, where both the computation of the similarity and the generation are based on pretrained vision-language models. Then, the phrase that generates the highest variation among the similarity scores is generated, using the same models. The next phrase maximizes the variance subject to being orthogonal, in the latent space, to the highest-variance phrase, and the process continues. Our experiments show that our method is able to convincingly capture the essence of image sets and describe the individual elements in a semantically meaningful way within the context of the entire set. Our code is available at: https://github.com/OdedH/textual-pca.

Causal discovery from observational and interventional data is challenging due to limited data and non-identifiability: factors that introduce uncertainty in estimating the underlying structural causal model (SCM). Selecting experiments (interventions) based on the uncertainty arising from both factors can expedite the identification of the SCM. Existing methods in experimental design for causal discovery from limited data either rely on linear assumptions for the SCM or select only the intervention target. This work incorporates recent advances in Bayesian causal discovery into the Bayesian optimal experimental design framework, allowing for active causal discovery of large, nonlinear SCMs while selecting both the interventional target and the value. We demonstrate the performance of the proposed method on synthetic graphs (Erdos-R\`enyi, Scale Free) for both linear and nonlinear SCMs as well as on the \emph{in-silico} single-cell gene regulatory network dataset, DREAM.

Today, computer systems hold large amounts of personal data. Yet while such an abundance of data allows breakthroughs in artificial intelligence, and especially machine learning (ML), its existence can be a threat to user privacy, and it can weaken the bonds of trust between humans and AI. Recent regulations now require that, on request, private information about a user must be removed from both computer systems and from ML models, i.e. ``the right to be forgotten''). While removing data from back-end databases should be straightforward, it is not sufficient in the AI context as ML models often `remember' the old data. Contemporary adversarial attacks on trained models have proven that we can learn whether an instance or an attribute belonged to the training data. This phenomenon calls for a new paradigm, namely machine unlearning, to make ML models forget about particular data. It turns out that recent works on machine unlearning have not been able to completely solve the problem due to the lack of common frameworks and resources. Therefore, this paper aspires to present a comprehensive examination of machine unlearning's concepts, scenarios, methods, and applications. Specifically, as a category collection of cutting-edge studies, the intention behind this article is to serve as a comprehensive resource for researchers and practitioners seeking an introduction to machine unlearning and its formulations, design criteria, removal requests, algorithms, and applications. In addition, we aim to highlight the key findings, current trends, and new research areas that have not yet featured the use of machine unlearning but could benefit greatly from it. We hope this survey serves as a valuable resource for ML researchers and those seeking to innovate privacy technologies. Our resources are publicly available at https://github.com/tamlhp/awesome-machine-unlearning.

For text classification tasks, finetuned language models perform remarkably well. Yet, they tend to rely on spurious patterns in training data, thus limiting their performance on out-of-distribution (OOD) test data. Among recent models aiming to avoid this spurious pattern problem, adding extra counterfactual samples to the training data has proven to be very effective. Yet, counterfactual data generation is costly since it relies on human annotation. Thus, we propose a novel solution that only requires annotation of a small fraction (e.g., 1%) of the original training data, and uses automatic generation of extra counterfactuals in an encoding vector space. We demonstrate the effectiveness of our approach in sentiment classification, using IMDb data for training and other sets for OOD tests (i.e., Amazon, SemEval and Yelp). We achieve noticeable accuracy improvements by adding only 1% manual counterfactuals: +3% compared to adding +100% in-distribution training samples, +1.3% compared to alternate counterfactual approaches.