The more extensive access to time-series data, especially for biomedical purposes, raises new methodological challenges, particularly regarding missing values. Functional linear discriminant analysis (FLDA) extends Linear Discriminant Analysis (LDA)-mediated multiclass classification and dimension reduction to data in the form of fragmented observations of a univariate function. For large multivariate and partially-observed data, there are two challenges: (i) statistical dependencies between different components of a multivariate function and (ii) heterogeneous sampling times with missing features. We here develop a multivariate version of FLDA, called MUDRA, to tackle these challenges and describe a computationally efficient expectation/conditional-maximisation (ECM) algorithm to infer its parameters without any tensor inversions. We assess its predictive power on the “Articulary Words” dataset and show its improvement over the state-of-the-art, especially in the case of missing data. This advancement in dimension reduction of multivariate functional data holds promise for enhancing classification accuracy in scenarios like partially observed short multivariate time series analysis.

In good arm identification (GAI), the goal is to identify one arm whose average performance exceeds a given threshold, referred to as a good arm, if it exists. Few works have studied GAI in the fixed-budget setting when the sampling budget is fixed beforehand, or in the anytime setting, when a recommendation can be asked at any time. We propose APGAI, an anytime and parameter-free sampling rule for GAI in stochastic bandits. APGAI can be straightforwardly used in fixed-confidence and fixed-budget settings. First, we derive upper bounds on its probability of error at any time. They show that adaptive strategies can be more efficient in detecting the absence of good arms than uniform sampling in several diverse instances. Second, when APGAI is combined with a stopping rule, we prove upper bounds on the expected sampling complexity, holding at any confidence level. Finally, we show the good empirical performance of APGAI on synthetic and real-world data. Our work offers an extensive overview of the GAI problem in all settings.

In the original publication of this article, the legend for Fig. 3 was inadvertently omitted in the published version.Specifically, the right-hand plot, depicting the performance of MUDRA on a synthetic dataset in terms of F1 score relative to the baseline ROCKET, was missing the legend identifying the respective models.For completeness and transparency, the incorrect and correct versions of Fig. 3 are presented with this correction article.The original article has been corrected.The original article can be found online at h t t p s : / / d o i . o r g / 1 0 . 1 0 0 7 / s 1 0 9 9 4 -0 2 5 -0 6 7 4 1 -0 .

BACKGROUND: Interpretability is a topical question in recommender systems, especially in healthcare applications. An interpretable classifier quantifies the importance of each input feature for the predicted item-user association in a non-ambiguous fashion. RESULTS: We introduce the novel Joint Embedding Learning-classifier for improved Interpretability (JELI). By combining the training of a structured collaborative-filtering classifier and an embedding learning task, JELI predicts new user-item associations based on jointly learned item and user embeddings while providing feature-wise importance scores. Therefore, JELI flexibly allows the introduction of priors on the connections between users, items, and features. In particular, JELI simultaneously (a) learns feature, item, and user embeddings; (b) predicts new item-user associations; (c) provides importance scores for each feature. Moreover, JELI instantiates a generic approach to training recommender systems by encoding generic graph-regularization constraints. CONCLUSIONS: First, we show that the joint training approach yields a gain in the predictive power of the downstream classifier. Second, JELI can recover feature-association dependencies. Finally, JELI induces a restriction in the number of parameters compared to baselines in synthetic and drug-repurposing data sets.

Abstract The more extensive access to time-series data, especially for biomedical purposes, raises new methodological challenges, particularly regarding missing values. Functional linear discriminant analysis (FLDA) extends Linear Discriminant Analysis (LDA)-mediated multiclass classification and dimension reduction to data in the form of fragmented observations of a univariate function. For large multivariate and partially-observed data, there are two challenges: (i) statistical dependencies between different components of a multivariate function and (ii) heterogeneous sampling times with missing features. We here develop a multivariate version of FLDA, called MUDRA, to tackle these challenges and describe a computationally efficient expectation/conditional-maximisation (ECM) algorithm to infer its parameters without any tensor inversions. We assess its predictive power on the “Articulary Words” dataset and show its improvement over the state-of-the-art, especially in the case of missing data. This advancement in dimension reduction of multivariate functional data holds promise for enhancing classification accuracy in scenarios like partially observed short multivariate time series analysis.

This paper introduces a general multi-agent bandit model in which each agent is facing a finite set of arms and may communicate with other agents through a central controller in order to identify -in pure exploration- or play -in regret minimization- its optimal arm. The twist is that the optimal arm for each agent is the arm with largest expected mixed reward, where the mixed reward of an arm is a weighted sum of the rewards of this arm for all agents. This makes communication between agents often necessary. This general setting allows to recover and extend several recent models for collaborative bandit learning, including the recently proposed federated learning with personalization [Shi et al., 2021]. In this paper, we provide new lower bounds on the sample complexity of pure exploration and on the regret. We then propose a near-optimal algorithm for pure exploration. This algorithm is based on phased elimination with two novel ingredients: a data-dependent sampling scheme within each phase, aimed at matching a relaxation of the lower bound.

Motivated by an application to drug repurposing, we propose the first algorithms to tackle the identification of the m ≥ 1 arms with largest means in a linear bandit model, in the fixed-confidence setting. These algorithms belong to the generic family of Gap-Index Focused Algorithms (GIFA) that we introduce for Top-m identification in linear bandits. We propose a unified analysis of these algorithms, which shows how the use of contexts might decrease the sample complexity. We further validate these algorithms empirically on simulated data and on a simple drug repurposing task.

We study the problem of the identification of m arms with largest means under a fixed error rate $\delta$ (fixed-confidence Top-m identification), for misspecified linear bandit models. This problem is motivated by practical applications, especially in medicine and recommendation systems, where linear models are popular due to their simplicity and the existence of efficient algorithms, but in which data inevitably deviates from linearity. In this work, we first derive a tractable lower bound on the sample complexity of any $\delta$-correct algorithm for the general Top-m identification problem. We show that knowing the scale of the deviation from linearity is necessary to exploit the structure of the problem. We then describe the first algorithm for this setting, which is both practical and adapts to the amount of misspecification. We derive an upper bound to its sample complexity which confirms this adaptivity and that matches the lower bound when $\delta \rightarrow 0$. Finally, we evaluate our algorithm on both synthetic and real-world data, showing competitive performance with respect to existing baselines.