We study calibration in question answering, estimating whether model correctly predicts answer for each question. Unlike prior work which mainly rely on the model's confidence score, our calibrator incorporates information about the input example (e.g., question and the evidence context). Together with data augmentation via back translation, our simple approach achieves 5-10% gains in calibration accuracy on reading comprehension benchmarks. Furthermore, we present the first calibration study in the open retrieval setting, comparing the calibration accuracy of retrieval-based span prediction models and answer generation models. Here again, our approach shows consistent gains over calibrators relying on the model confidence. Our simple and efficient calibrator can be easily adapted to many tasks and model architectures, showing robust gains in all settings.

In this paper, we study the convergence properties of off-policy policy improvement algorithms with state-action density ratio correction under function approximation setting, where the objective function is formulated as a max-max-min optimization problem. We characterize the bias of the learning objective and present two strategies with finite-time convergence guarantees. In our first strategy, we present algorithm P-SREDA with convergence rate $O(\epsilon^{-3})$, whose dependency on $\epsilon$ is optimal. In our second strategy, we propose a new off-policy actor-critic style algorithm named O-SPIM. We prove that O-SPIM converges to a stationary point with total complexity $O(\epsilon^{-4})$, which matches the convergence rate of some recent actor-critic algorithms in the on-policy setting.

Partial-label learning (PLL) generally focuses on inducing a noise-tolerant multi-class classifier by training on overly-annotated samples, each of which is annotated with a set of labels, but only one is the valid label. A basic promise of existing PLL solutions is that there are sufficient partial-label (PL) samples for training. However, it is more common than not to have just few PL samples at hand when dealing with new tasks. Furthermore, existing few-shot learning algorithms assume precise labels of the support set; as such, irrelevant labels may seriously mislead the meta-learner and thus lead to a compromised performance. How to enable PLL under a few-shot learning setting is an important problem, but not yet well studied. In this paper, we introduce an approach called FsPLL (Few-shot PLL). FsPLL first performs adaptive distance metric learning by an embedding network and rectifying prototypes on the tasks previously encountered. Next, it calculates the prototype of each class of a new task in the embedding network. An unseen example can then be classified via its distance to each prototype. Experimental results on widely-used few-shot datasets (Omniglot and miniImageNet) demonstrate that our FsPLL can achieve a superior performance than the state-of-the-art methods across different settings, and it needs fewer samples for quickly adapting to new tasks.

S{\o}gaard (2020) obtained results suggesting the fraction of trees occurring in the test data isomorphic to trees in the training set accounts for a non-trivial variation in parser performance. Similar to other statistical analyses in NLP, the results were based on evaluating linear regressions. However, the study had methodological issues and was undertaken using a small sample size leading to unreliable results. We present a replication study in which we also bin sentences by length and find that only a small subset of sentences vary in performance with respect to graph isomorphism. Further, the correlation observed between parser performance and graph isomorphism in the wild disappears when controlling for covariants. However, in a controlled experiment, where covariants are kept fixed, we do observe a strong correlation. We suggest that conclusions drawn from statistical analyses like this need to be tempered and that controlled experiments can complement them by more readily teasing factors apart.

Despite their ubiquity in core AI fields like natural language processing, the mechanics of deep attention-based neural networks like the Transformer model are not fully understood. In this article, we present a new perspective towards understanding how Transformers work. In particular, we show that the "dot-product attention" that is the core of the Transformer's operation can be characterized as a kernel learning method on a pair of Banach spaces. In particular, the Transformer's kernel is characterized as having an infinite feature dimension. Along the way we consider an extension of the standard kernel learning problem to a binary setting, where data come from two input domains and a response is defined for every cross-domain pair. We prove a new representer theorem for these binary kernel machines with non-Mercer (indefinite, asymmetric) kernels (implying that the functions learned are elements of reproducing kernel Banach spaces rather than Hilbert spaces), and also prove a new universal approximation theorem showing that the Transformer calculation can learn any binary non-Mercer reproducing kernel Banach space pair. We experiment with new kernels in Transformers, and obtain results that suggest the infinite dimensionality of the standard Transformer kernel is partially responsible for its performance. This paper's results provide a new theoretical understanding of a very important but poorly understood model in modern machine~learning.

In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods often impose some specific model structures such as linear models or additive models, and assume independent data observations. Our proposed test instead allows the associations among the random variables to be nonlinear and the data to be time-dependent. We build the test based on some highly flexible neural networks learners. We establish the asymptotic guarantees of the test, while allowing either the number of subjects or the number of time points for each subject to diverge to infinity. We demonstrate the efficacy of the test through simulations and a brain connectivity network analysis.

Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. Through new insights into the manifold geometry underlying a generic latent position model, we show that this can be accomplished in two steps: matrix factorisation, followed by nonlinear dimension reduction. This combination is effective because the point cloud obtained in the first step lives close to a manifold in which latent distance is encoded as geodesic distance. Hence, a nonlinear dimension reduction tool, approximating geodesic distance, can recover the latent positions, up to a simple transformation. We give a detailed account of the case where spectral embedding is used, followed by Isomap, and provide encouraging experimental evidence for other combinations of techniques.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system $\bar{A}\theta = \bar{b}$ for which $\bar{A}$ and $\bar{b}$ can only be accessed through random estimates $\{({\bf A}_n, {\bf b}_n): n \in \mathbb{N}^*\}$. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence $\{({\bf A}_n, {\bf b}_n): n \in \mathbb{N}^*\}$ than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices $\{{\bf A}_n: n \in \mathbb{N}^*\}$, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

The ability to compare and align related datasets living in heterogeneous spaces plays an increasingly important role in machine learning. The Gromov-Wasserstein (GW) formalism can help tackle this problem. Its main goal is to seek an assignment (more generally a coupling matrix) that can register points across otherwise incomparable datasets. As a non-convex and quadratic generalization of optimal transport (OT), GW is NP-hard. Yet, heuristics are known to work reasonably well in practice, the state of the art approach being to solve a sequence of nested regularized OT problems. While popular, that heuristic remains too costly to scale, with cubic complexity in the number of samples $n$. We show in this paper how a recent variant of the Sinkhorn algorithm can substantially speed up the resolution of GW. That variant restricts the set of admissible couplings to those admitting a low rank factorization as the product of two sub-couplings. By updating alternatively each sub-coupling, our algorithm computes a stationary point of the problem in quadratic time with respect to the number of samples. When cost matrices have themselves low rank, our algorithm has time complexity $\mathcal{O}(n)$. We demonstrate the efficiency of our method on simulated and real data.

We investigate the connections between sparse approximation methods for making kernel methods and Gaussian processes (GPs) scalable to massive data, focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes (SVGP). While sparse approximation methods for GPs and kernel methods share some algebraic similarities, the literature lacks a deep understanding of how and why they are related. This is a possible obstacle for the communications between the GP and kernel communities, making it difficult to transfer results from one side to the other. Our motivation is to remove this possible obstacle, by clarifying the connections between the sparse approximations for GPs and kernel methods. In this work, we study the two popular approaches, the Nystr\"om and SVGP approximations, in the context of a regression problem, and establish various connections and equivalences between them. In particular, we provide an RKHS interpretation of the SVGP approximation, and show that the Evidence Lower Bound of the SVGP contains the objective function of the Nystr\"om approximation, revealing the origin of the algebraic equivalence between the two approaches. We also study recently established convergence results for the SVGP and how they are related to the approximation quality of the Nystr\"om method.