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Natural language tasks like Named Entity Recognition (NER) in the clinical domain on non-English texts can be very time-consuming and expensive due to the lack of annotated data. Cross-lingual transfer (CLT) is a way to circumvent this issue thanks to the ability of multilingual large language models to be fine-tuned on a specific task in one language and to provide high accuracy for the same task in another language. However, other methods leveraging translation models can be used to perform NER without annotated data in the target language, by either translating the training set or test set. This paper compares cross-lingual transfer with these two alternative methods, to perform clinical NER in French and in German without any training data in those languages. To this end, we release MedNERF a medical NER test set extracted from French drug prescriptions and annotated with the same guidelines as an English dataset. Through extensive experiments on this dataset and on a German medical dataset (Frei and Kramer, 2021), we show that translation-based methods can achieve similar performance to CLT but require more care in their design. And while they can take advantage of monolingual clinical language models, those do not guarantee better results than large general-purpose multilingual models, whether with cross-lingual transfer or translation., Comment: 23 pages, Proceedings of the 5th Clinical Natural Language Processing Workshop

In this paper, we investigate the limiting behavior of a continuous-time counterpart of the Stochastic Gradient Descent (SGD) algorithm applied to two-layer overparameterized neural networks, as the number or neurons (ie, the size of the hidden layer) $N \to +\infty$. Following a probabilistic approach, we show 'propagation of chaos' for the particle system defined by this continuous-time dynamics under different scenarios, indicating that the statistical interaction between the particles asymptotically vanishes. In particular, we establish quantitative convergence with respect to $N$ of any particle to a solution of a mean-field McKean-Vlasov equation in the metric space endowed with the Wasserstein distance. In comparison to previous works on the subject, we consider settings in which the sequence of stepsizes in SGD can potentially depend on the number of neurons and the iterations. We then identify two regimes under which different mean-field limits are obtained, one of them corresponding to an implicitly regularized version of the minimization problem at hand. We perform various experiments on real datasets to validate our theoretical results, assessing the existence of these two regimes on classification problems and illustrating our convergence results.

This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes. First, we show that the recursion defining SGD can be provably approximated by solutions of a time inhomogeneous Stochastic Differential Equation (SDE) using an appropriate coupling. In the specific case of a batch noise we refine our results using recent advances in Stein's method. Then, motivated by recent analyses of deterministic and stochastic optimization methods by their continuous counterpart, we study the long-time behavior of the continuous processes at hand and establish non-asymptotic bounds. To that purpose, we develop new comparison techniques which are of independent interest. Adapting these techniques to the discrete setting, we show that the same results hold for the corresponding SGD sequences. In our analysis, we notably improve non-asymptotic bounds in the convex setting for SGD under weaker assumptions than the ones considered in previous works. Finally, we also establish finite-time convergence results under various conditions, including relaxations of the famous {\L}ojasiewicz inequality, which can be applied to a class of non-convex functions., Comment: 94 pages, 4 figures

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate $\hat{\beta}$ of the hidden parameter $\beta^{\star}$ of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of $T$ samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the $\ell^2$-loss $\mathbb{E} [\lVert\hat{\beta}-\beta^{\star}\rVert^2]$ the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a $\mathcal{O}(T^{-2})$ regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings., Comment: 29 pages, 5 figures

We consider the classical problem of sequential resource allocation where a decision maker must repeatedly divide a budget between several resources, each with diminishing returns. This can be recast as a specific stochastic optimization problem where the objective is to maximize the cumulative reward, or equivalently to minimize the regret. We construct an algorithm that is {\em adaptive} to the complexity of the problem, expressed in term of the regularity of the returns of the resources, measured by the exponent in the {\L}ojasiewicz inequality (or by their universal concavity parameter). Our parameter-independent algorithm recovers the optimal rates for strongly-concave functions and the classical fast rates of multi-armed bandit (for linear reward functions). Moreover, the algorithm improves existing results on stochastic optimization in this regret minimization setting for intermediate cases., Comment: ALT2020, 45 pages, 9 figures

We consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy which is known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting the context space into bins, and solving simultaneously - and independently - regularized multi-armed bandit instances on each bin. We derive slow and fast rates of convergence, depending on the unknown complexity of the problem. We also consider a new relevant margin condition to get problem-independent convergence rates, ending up in intermediate convergence rates interpolating between the aforementioned slow and fast rates., Comment: AISTATS 2019, 23 pages, 2 figures