We propose a transductive meta-learning method that uses unlabelled instances to improve few-shot image classification performance. Our approach combines a regularized Mahalanobis-distance-based soft k-means clustering procedure with a modified state of the art neural adaptive feature extractor to achieve improved test-time classification accuracy using unlabelled data. We evaluate our method on transductive few-shot learning tasks, in which the goal is to jointly predict labels for query (test) examples given a set of support (training) examples. We achieve new state of the art performance on Meta-Dataset, and produce competitive results on mini-and tiered-ImageNet benchmarks. Deep learning has revolutionized visual classification, enabled in part by the development of large and diverse sets of curated training data (Szegedy et al., 2014; He et al., 2015; Krizhevsky et al., 2017; Simonyan & Zisserman, 2014; Sornam et al., 2017). However, in many image classification settings, millions of labelled examples are not available; therefore, techniques that can achieve sufficient classification performance with few labels are required. This has motivated research on few-shot learning (Feyjie et al., 2020; Wang & Yao, 2019; Wang et al., 2019; Bellet et al., 2013), which seeks to develop methods for developing classifiers with much smaller datasets.

Label smoothing regularization (LSR) has a great success in training deep neural networks by stochastic algorithms such as stochastic gradient descent and its variants. However, the theoretical understanding of its power from the view of optimization is still rare. This study opens the door to a deep understanding of LSR by initiating the analysis. In this paper, we analyze the convergence behaviors of stochastic gradient descent with label smoothing regularization for solving non-convex problems and show that an appropriate LSR can help to speed up the convergence by reducing the variance. More interestingly, we proposed a simple yet effective strategy, namely Two-Stage LAbel smoothing algorithm (TSLA), that uses LSR in the early training epochs and drops it off in the later training epochs. We observe from the improved convergence result of TSLA that it benefits from LSR in the first stage and essentially converges faster in the second stage. To the best of our knowledge, this is the first work for understanding the power of LSR via establishing convergence complexity of stochastic methods with LSR in non-convex optimization. We empirically demonstrate the effectiveness of the proposed method in comparison with baselines on training ResNet models over benchmark data sets.

The study of deep networks (DNs) in the infinite-width limit, via the so-called Neural Tangent Kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DN architecture remains to be kernelized, namely, the Recurrent Neural Network (RNN). In this paper we introduce and study the Recurrent Neural Tangent Kernel (RNTK), which sheds new insights into the behavior of overparametrized RNNs, including how different time steps are weighted by the RNTK to form the output under different initialization parameters and nonlinearity choices, and how inputs of different lengths are treated. We demonstrate via a number of experiments that the RNTK offers significant performance gains over other kernels, including standard NTKs across a range of different data sets. A unique benefit of the RNTK is that it is agnostic to the length of the input, in stark contrast to other kernels.

In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which concerns coding schemes where the replication factor of the data is too low to recover the full gradient exactly. Our work is motivated by the challenge of creating approximate gradient coding schemes that simultaneously work well in both the adversarial and stochastic models. To that end, we introduce novel approximate gradient codes based on expander graphs, in which each machine receives exactly two blocks of data points. We analyze the decoding error both in the random and adversarial straggler setting, when optimal decoding coefficients are used. We show that in the random setting, our schemes achieve an error to the gradient that decays exponentially in the replication factor. In the adversarial setting, the error is nearly a factor of two smaller than any existing code with similar performance in the random setting. We show convergence bounds both in the random and adversarial setting for gradient descent under standard assumptions using our codes. In the random setting, our convergence rate improves upon block-box bounds. In the adversarial setting, we show that gradient descent can converge down to a noise floor that scales linearly with the adversarial error to the gradient. We demonstrate empirically that our schemes achieve near-optimal error in the random setting and converge faster than algorithms which do not use the optimal decoding coefficients.

Adaptive gradient methods are typically used for training over-parameterized models capable of exactly fitting the data; we thus study their convergence in this interpolation setting. Under an interpolation assumption, we prove that AMSGrad with a constant step-size and momentum can converge to the minimizer at the faster $O(1/T)$ rate for smooth, convex functions. Furthermore, in this setting, we show that AdaGrad can achieve an $O(1)$ regret in the online convex optimization framework. When interpolation is only approximately satisfied, we show that constant step-size AMSGrad converges to a neighbourhood of the solution. On the other hand, we prove that AdaGrad is robust to the violation of interpolation and converges to the minimizer at the optimal rate. However, we demonstrate that even for simple, convex problems satisfying interpolation, the empirical performance of these methods heavily depends on the step-size and requires tuning. We alleviate this problem by using stochastic line-search (SLS) and Polyak's step-sizes (SPS) to help these methods adapt to the function's local smoothness. By using these techniques, we prove that AdaGrad and AMSGrad do not require knowledge of problem-dependent constants and retain the convergence guarantees of their constant step-size counterparts. Experimentally, we show that these techniques help improve the convergence and generalization performance across tasks, from binary classification with kernel mappings to classification with deep neural networks.

The elastic-net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its nice properties originate from a combination of $\ell_1$ and $\ell_2$ norms, which endow this method with the ability to select variables taking into account the correlations between them. In the last few years, semi-supervised approaches, that use both labeled and unlabeled data, have become an important component in the statistical research. Despite this interest, however, few researches have investigated semi-supervised elastic-net extensions. This paper introduces a novel solution for semi-supervised learning of sparse features in the context of generalized linear model estimation: the generalized semi-supervised elastic-net (s2net), which extends the supervised elastic-net method, with a general mathematical formulation that covers, but is not limited to, both regression and classification problems. We develop a flexible and fast implementation for s2net in R, and its advantages are illustrated using both real and synthetic data sets.

Robust optimization has been widely used in nowadays data science, especially in adversarial training. However, little research has been done to quantify how robust optimization changes the optimizers and the prediction losses comparing to standard training. In this paper, inspired by the influence function in robust statistics, we introduce the Adversarial Influence Function (AIF) as a tool to investigate the solution produced by robust optimization. The proposed AIF enjoys a closed-form and can be calculated efficiently. To illustrate the usage of AIF, we apply it to study model sensitivity -- a quantity defined to capture the change of prediction losses on the natural data after implementing robust optimization. We use AIF to analyze how model complexity and randomized smoothing affect the model sensitivity with respect to specific models. We further derive AIF for kernel regressions, with a particular application to neural tangent kernels, and experimentally demonstrate the effectiveness of the proposed AIF. Lastly, the theories of AIF will be extended to distributional robust optimization.

In real world applications of supervised learning methods, training and test sets are often sampled from the distinct distributions and we must resort to domain adaptation techniques. One special class of techniques is Covariate Shift Adaptation, which allows practitioners to obtain good generalization performance in the distribution of interest when domains differ only by the marginal distribution of features. Traditionally, Covariate Shift Adaptation is implemented using Importance Weighting which may fail in high-dimensional settings due to small Effective Sample Sizes (ESS). In this paper, we propose (i) a connection between ESS, high-dimensional settings and generalization bounds and (ii) a simple, general and theoretically sound approach to combine feature selection and Covariate Shift Adaptation. The new approach yields good performance with improved ESS.

Optimization is essentially everywhere and most real-world problems are of nonlinear and multimodal nature, i.e., there may exist multiple local optima that become traps for local search [23]. That is, classical local search based on gradient descent will get stuck in local optima unless restart mechanisms or search space exploration methods prevent premature convergence. Much effort has been put into this issue. Early attempts tried to make local search more flexible, e.g., by adding search points or spanning simplex structures, to discover patterns in search space and allow non-derivative descent to the optimum [20]. However, local search cannot solve these problems in general. Thus, later approaches [1] combine originally one-dimensional global search mechanisms like the STEP global search [30] and a local interpolation technique proposed by Brent [3] for the multivariate case. Others combine established stochastic global search mechanisms based on clustering [24] with newer elements of global optimizers [29] to gain quality improvements of solutions and to avoid finding only local optima [22].

Lexical semantic change detection (also known as semantic shift tracing) is a task of identifying words that have changed their meaning over time. Unsupervised semantic shift tracing, focal point of SemEval2020, is particularly challenging. Given the unsupervised setup, in this work, we propose to identify clusters among different occurrences of each target word, considering these as representatives of different word meanings. As such, disagreements in obtained clusters naturally allow to quantify the level of semantic shift per each target word in four target languages. To leverage this idea, clustering is performed on contextualized (BERT-based) embeddings of word occurrences. The obtained results show that our approach performs well both measured separately (per language) and overall, where we surpass all provided SemEval baselines.