Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear eigenvalue problems, and in electronic structures computations, to name a few problems. In statistics and machine learning, they arise, for example, in various dimensionality reduction techniques such as canonical correlation analysis. In deep learning, regularization and improved stability can be obtained by constraining some layers to have parameter matrices that belong to the Stiefel manifold. Solving problems on the generalized Stiefel manifold can be approached via the tools of Riemannian optimization. However, using the standard geometric components for the generalized Stiefel manifold has two possible shortcomings: computing some of the geometric components can be too expensive and convergence can be rather slow in certain cases. Both shortcomings can be addressed using a technique called Riemannian preconditioning, which amounts to using geometric components derived by a precoditioner that defines a Riemannian metric on the constraint manifold. In this paper we develop the geometric components required to perform Riemannian optimization on the generalized Stiefel manifold equipped with a non-standard metric, and illustrate theoretically and numerically the use of those components and the effect of Riemannian preconditioning for solving optimization problems on the generalized Stiefel manifold.

Quantification, variously called "supervised prevalence estimation" or "learning to quantify", is the supervised learning task of generating predictors of the relative frequencies (a.k.a. "prevalence values") of the classes of interest in unlabelled data samples. While many quantification methods have been proposed in the past for binary problems and, to a lesser extent, single-label multiclass problems, the multi-label setting (i.e., the scenario in which the classes of interest are not mutually exclusive) remains by and large unexplored. A straightforward solution to the multi-label quantification problem could simply consist of recasting the problem as a set of independent binary quantification problems. Such a solution is simple but na\"ive, since the independence assumption upon which it rests is, in most cases, not satisfied. In these cases, knowing the relative frequency of one class could be of help in determining the prevalence of other related classes. We propose the first truly multi-label quantification methods, i.e., methods for inferring estimators of class prevalence values that strive to leverage the stochastic dependencies among the classes of interest in order to predict their relative frequencies more accurately. We show empirical evidence that natively multi-label solutions outperform the na\"ive approaches by a large margin. The code to reproduce all our experiments is available online.

We consider the problem of parameter estimation under local information constraints, where the estimation algorithm has access to only limited information about each sample. These constraints can be of various types, including communication constraints, where each sample must be described using a few (e.g., constant number of) bits; (local) privacy constraints, where each sample is obtained from a different user and the users seek to reveal as little as possible about their specific data; as well as many others, e.g., noisy communication channels, or limited types of data access such as linear measurements. Such problems have received a lot of attention in recent years, motivated by applications such as data analytics in distributed systems and federated learning. Our main focus is on information-theoretic lower bounds for the minimax error rates (or, equivalently, the sample complexity) of these problems. Several recent works have provided different bounds that apply to specific constraints or work for specific parametric estimation problems, sometimes without allowing for interactive protocols. Indeed, handling interactive protocols is technically challenging, and several results in prior work exhibit flaws in their analysis. In particular, even the most basic Gaussian mean estimation problem using interactive communication remains, quite surprisingly, open. We present general, "plug-and-play" lower bounds for parametric estimation under information constraints that can be used for any local information constraint and allows for interactive protocols. Our abstract bound requires very simple (and natural) assumptions to hold for the underlying parametric family; in particular, we do not require technical "regularity" conditions that are common in asymptotic statistics.

In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to reduce the input data via Principal Component Analysis (PCA). Since there exists a theorem by Ding and He that links the cardinality of the optimal clusters found with K-Means and the cardinality of the selected informative PCA components, the computational experiments tested the theorem between two quantitative features selection methods: Kaiser criteria (based on imperative decision) versus Wishart criteria (based on random matrix theory). The results suggested that PCA reduction with features selection by Wishart criteria leads to a low matrix condition number and satisfies the relation between clusters and components predicts by the theorem. The data used for the computations are from a neuroscientific repository: it regards healthy and young subjects that performed a task-oriented functional Magnetic Resonance Imaging (fMRI) paradigm.

As the aging of society continues to accelerate, Alzheimer's Disease (AD) has received more and more attention from not only medical but also other fields, such as computer science, over the past decade. Since speech is considered one of the effective ways to diagnose cognitive decline, AD detection from speech has emerged as a hot topic. Nevertheless, such approaches fail to tackle several key issues: 1) AD is a complex neurocognitive disorder which means it is inappropriate to conduct AD detection using utterance information alone while ignoring dialogue information; 2) Utterances of AD patients contain many disfluencies that affect speech recognition yet are helpful to diagnosis; 3) AD patients tend to speak less, causing dialogue breakdown as the disease progresses. This fact leads to a small number of utterances, which may cause detection bias. Therefore, in this paper, we propose a novel AD detection architecture consisting of two major modules: an ensemble AD detector and a proactive listener. This architecture can be embedded in the dialogue system of conversational robots for healthcare.

Building models that can be rapidly adapted to novel tasks using only a handful of annotated examples is an open challenge for multimodal machine learning research. We introduce Flamingo, a family of Visual Language Models (VLM) with this ability. We propose key architectural innovations to: (i) bridge powerful pretrained vision-only and language-only models, (ii) handle sequences of arbitrarily interleaved visual and textual data, and (iii) seamlessly ingest images or videos as inputs. Thanks to their flexibility, Flamingo models can be trained on large-scale multimodal web corpora containing arbitrarily interleaved text and images, which is key to endow them with in-context few-shot learning capabilities. We perform a thorough evaluation of our models, exploring and measuring their ability to rapidly adapt to a variety of image and video tasks. These include open-ended tasks such as visual question-answering, where the model is prompted with a question which it has to answer; captioning tasks, which evaluate the ability to describe a scene or an event; and close-ended tasks such as multiple-choice visual question-answering. For tasks lying anywhere on this spectrum, a single Flamingo model can achieve a new state of the art with few-shot learning, simply by prompting the model with task-specific examples. On numerous benchmarks, Flamingo outperforms models fine-tuned on thousands of times more task-specific data.

Small and medium enterprises rely on detailed Web analytics to be informed about their market and competition. Focused crawlers meet this demand by crawling and indexing specific parts of the Web. Critically, a focused crawler must quickly find new pages that have not yet been indexed. Since a new page can be discovered only by following a new outlink, predicting new outlinks is very relevant in practice. In the literature, many feature designs have been proposed for predicting changes in the Web. In this work we provide a structured analysis of this problem, using new outlinks as our running prediction target. Specifically, we unify earlier feature designs in a taxonomic arrangement of features along two dimensions: static versus dynamic features, and features of a page versus features of the network around it. Within this taxonomy, complemented by our new (mainly, dynamic network) features, we identify best predictors for new outlinks. Our main conclusion is that most informative features are the recent history of new outlinks on a page itself, and of its content-related pages. Hence, we propose a new 'look back, look around' (LBLA) model, that uses only these features. With the obtained predictions, we design a number of scoring functions to guide a focused crawler to pages with most new outlinks, and compare their performance. The LBLA approach proved extremely effective, outperforming other models including those that use a most complete set of features. One of the learners we use, is the recent NGBoost method that assumes a Poisson distribution for the number of new outlinks on a page, and learns its parameters. This connects the two so far unrelated avenues in the literature: predictions based on features of a page, and those based on probabilistic modelling. All experiments were carried out on an original dataset, made available by a commercial focused crawler.

Traditional evaluation metrics for classification in natural language processing such as accuracy and area under the curve fail to differentiate between models with different predictive behaviors despite their similar performance metrics. We introduce sensitivity score, a metric that scrutinizes models' behaviors at the vocabulary level to provide insights into disparities in their decision-making logic. We assess the sensitivity score on a set of representative words in the test set using two classifiers trained for hospital readmission classification with similar performance statistics. Our experiments compare the decision-making logic of clinicians and classifiers based on rank correlations of sensitivity scores. The results indicate that the language model's sensitivity score aligns better with the professionals than the xgboost classifier on tf-idf embeddings, which suggests that xgboost uses some spurious features. Overall, this metric offers a novel perspective on assessing models' robustness by quantifying their discrepancy with professional opinions. Our code is available on GitHub (https://github.com/nyuolab/Model_Sensitivity).

Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types ("marks"), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior modeling. Since these data are typically modeled autoregressively (e.g., using neural Hawkes processes or their classical counterparts), it is natural to ask questions about future scenarios such as "what kind of event will occur next" or "will an event of type $A$ occur before one of type $B$". Unfortunately, some of these queries are notoriously hard to address since current methods are limited to naive simulation, which can be highly inefficient. This paper introduces a new typology of query types and a framework for addressing them using importance sampling. Example queries include predicting the $n^\text{th}$ event type in a sequence and the hitting time distribution of one or more event types. We also leverage these findings further to be applicable for estimating general "$A$ before $B$" type of queries. We prove theoretically that our estimation method is effectively always better than naive simulation and show empirically based on three real-world datasets that it is on average 1,000 times more efficient than existing approaches.

Few-Shot Text Classification (FSTC) imitates humans to learn a new text classifier efficiently with only few examples, by leveraging prior knowledge from historical tasks. However, most prior works assume that all the tasks are sampled from a single data source, which cannot adapt to real-world scenarios where tasks are heterogeneous and lie in different distributions. As such, existing methods may suffer from their globally knowledge-shared mechanisms to handle the task heterogeneity. On the other hand, inherent task relation are not explicitly captured, making task knowledge unorganized and hard to transfer to new tasks. Thus, we explore a new FSTC setting where tasks can come from a diverse range of data sources. To address the task heterogeneity, we propose a self-supervised hierarchical task clustering (SS-HTC) method. SS-HTC not only customizes cluster-specific knowledge by dynamically organizing heterogeneous tasks into different clusters in hierarchical levels but also disentangles underlying relations between tasks to improve the interpretability. Extensive experiments on five public FSTC benchmark datasets demonstrate the effectiveness of SS-HTC.