We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be parallelized across multiple independent tasks. Our main contribution is to demonstrate that the convergence of these methods can significantly be improved by a randomization technique which corresponds to repartitioning coordinates across tasks during the optimization procedure. We provide a theoretical analysis that accurately characterizes the expected convergence gains of repartitioning and validate our findings empirically on various traditional machine learning tasks. From an implementation perspective, block-separable models are well suited for parallelization and, when shared memory is available, randomization can be implemented on top of existing methods very efficiently to improve convergence.

Kernel functions are a powerful tool to enhance the $k$-means clustering algorithm via the kernel trick. It is known that the parameters of the chosen kernel function can have a dramatic impact on the result. In supervised settings, these can be tuned via cross-validation, but for clustering this is not straightforward and heuristics are usually employed. In this paper we study the impact of kernel parameters on kernel $k$-means. In particular, we derive a lower bound, tight up to constant factors, below which the parameter of the RBF kernel will render kernel $k$-means meaningless. We argue that grid search can be ineffective for hyperparameter search in this context and propose an alternative algorithm for this purpose. In addition, we offer an efficient implementation based on fast approximate exponentiation with provable quality guarantees. Our experimental results demonstrate the ability of our method to efficiently reveal a rich and useful set of hyperparameter values.

We propose Differentiable Window, a new neural module and general purpose component for dynamic window selection. While universally applicable, we demonstrate a compelling use case of utilizing Differentiable Window to improve standard attention modules by enabling more focused attentions over the input regions. We propose two variants of Differentiable Window, and integrate them within the Transformer architecture in two novel ways. We evaluate our proposed approach on a myriad of NLP tasks, including machine translation, sentiment analysis, subject-verb agreement and language modeling. Our experimental results demonstrate consistent and sizable improvements across all tasks.

Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: any loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of underfitting. To address this, we propose a framework to build robust loss functions called Active Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.

We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local differential privacy noise. The ambiguity set is shown to contain the probability distribution of unperturbed, clean data. The radius of the ambiguity set is a function of the privacy budget, spread of the data, and the size of the problem. Hence, machine learning with locally-differentially private datasets can be rewritten as a distributionally-robust optimization. For general distributions, the distributionally-robust optimization problem can relaxed as a regularized machine learning problem with the Lipschitz constant of the machine learning model as a regularizer. For linear and logistic regression, this regularizer is the dual norm of the model parameters. For Gaussian data, the distributionally-robust optimization problem can be solved exactly to find an optimal regularizer. This approach results in an entirely new regularizer for training linear regression models. Training with this novel regularizer can be posed as a semi-definite program. Finally, the performance of the proposed distributionally-robust machine learning training is demonstrated on practical datasets.

Recently, deep learning have achieved promising results in Estimated Time of Arrival (ETA), which is considered as predicting the travel time from the origin to the destination along a given path. One of the key techniques is to use embedding vectors to represent the elements of road network, such as the links (road segments). However, the embedding suffers from the data sparsity problem that many links in the road network are traversed by too few floating cars even in large ride-hailing platforms like Uber and DiDi. Insufficient data makes the embedding vectors in an under-fitting status, which undermines the accuracy of ETA prediction. To address the data sparsity problem, we propose the Road Network Metric Learning framework for ETA (RNML-ETA). It consists of two components: (1) a main regression task to predict the travel time, and (2) an auxiliary metric learning task to improve the quality of link embedding vectors. We further propose the triangle loss, a novel loss function to improve the efficiency of metric learning. We validated the effectiveness of RNML-ETA on large scale real-world datasets, by showing that our method outperforms the state-of-the-art model and the promotion concentrates on the cold links with few data.

Continuous submodular functions are a category of generally non-convex/non-concave functions with a wide spectrum of applications. The celebrated property of this class of functions - continuous submodularity - enables both exact minimization and approximate maximization in poly. time. Continuous submodularity is obtained by generalizing the notion of submodularity from discrete domains to continuous domains. It intuitively captures a repulsive effect amongst different dimensions of the defined multivariate function. In this paper, we systematically study continuous submodularity and a class of non-convex optimization problems: continuous submodular function maximization. We start by a thorough characterization of the class of continuous submodular functions, and show that continuous submodularity is equivalent to a weak version of the diminishing returns (DR) property. Thus we also derive a subclass of continuous submodular functions, termed continuous DR-submodular functions, which enjoys the full DR property. Then we present operations that preserve continuous (DR-)submodularity, thus yielding general rules for composing new submodular functions. We establish intriguing properties for the problem of constrained DR-submodular maximization, such as the local-global relation. We identify several applications of continuous submodular optimization, ranging from influence maximization, MAP inference for DPPs to provable mean field inference. For these applications, continuous submodularity formalizes valuable domain knowledge relevant for optimizing this class of objectives. We present inapproximability results and provable algorithms for two problem settings: constrained monotone DR-submodular maximization and constrained non-monotone DR-submodular maximization. Finally, we extensively evaluate the effectiveness of the proposed algorithms.

Motivated by broad applications in reinforcement learning and federated learning, we study local stochastic approximation over a network of agents, where their goal is to find the root of an operator composed of the local operators at the agents. Our focus is to characterize the finite-time performance of this method when the data at each agent are generated from Markov processes, and hence they are dependent. In particular, we provide the convergence rates of local stochastic approximation for both constant and time-varying step sizes. Our results show that these rates are within a logarithmic factor of the ones under independent data. We then illustrate the applications of these results to different interesting problems in multi-task reinforcement learning and federated learning.

Point clouds have been recognized as a crucial data structure for 3D content and are essential in a number of applications such as virtual and mixed reality, autonomous driving, cultural heritage, etc. In this paper, we propose a set of contributions to improve deep point cloud compression, i.e.: using a scale hyperprior model for entropy coding; employing deeper transforms; a different balancing weight in the focal loss; optimal thresholding for decoding; and sequential model training. In addition, we present an extensive ablation study on the impact of each of these factors, in order to provide a better understanding about why they improve RD performance. An optimal combination of the proposed improvements achieves BD-PSNR gains over G-PCC trisoup and octree of 5.50 (6.48) dB and 6.84 (5.95) dB, respectively, when using the point-to-point (point-to-plane) metric. Code is available at https://github.com/mauriceqch/pcc_geo_cnn_v2 .

In this paper, we introduce the Dissimilarity Mixture Autoencoder (DMAE), a novel neural network model that uses a dissimilarity function to generalize a family of density estimation and clustering methods. It is formulated in such a way that it internally estimates the parameters of a probability distribution through gradient-based optimization. Also, the proposed model can leverage from deep representation learning due to its straightforward incorporation into deep learning architectures, because, it consists of an encoder-decoder network that computes a probabilistic representation. Experimental evaluation was performed on image and text clustering benchmark datasets showing that the method is competitive in terms of unsupervised classification accuracy and normalized mutual information. The source code to replicate the experiments is publicly available at https://github.com/larajuse/DMAE