A more formal discussion explanatory variables is of high practical importance is provided in Section 2. in many disciplines. Recent work exploits stability of regression coefficients or invariance However most state of the art methods suffer from scalability properties of models across different experimental problems since they scan all potential subsets of variables conditions for reconstructing the full causal and test whether the conditional distribution of Y given graph. These approaches generally do not scale a subset of variables is invariant across all environments well with the number of the explanatory variables (Peters et al., 2016) . This search is hence exponential in and are difficult to extend to nonlinear relationships. the number of covariates; the methods, while maintaining Contrary to existing work, we propose an appealing theoretical guarantees, are thus already computationally approach which even works for observational data hard for graphs of ten variables, and get infeasible alone, while still offering theoretical guarantees for larger graphs, unless one resorts to heuristic procedures.

The recent advances in sensor technologies and smart devices enable the collaborative collection of a sheer volume of data from multiple information sources. As a promising tool to efficiently extract useful information from such big data, machine learning has been pushed to the forefront and seen great success in a wide range of relevant areas such as computer vision, health care, and financial market analysis. To accommodate the large volume of data, there is a surge of interest in the design of distributed machine learning, among which stochastic gradient descent (SGD) is one of the mostly adopted methods. Nonetheless, distributed machine learning methods may be vulnerable to Byzantine attack, in which the adversary can deliberately share falsified information to disrupt the intended machine learning procedures. Therefore, two asynchronous Byzantine tolerant SGD algorithms are proposed in this work, in which the honest collaborative workers are assumed to store the model parameters derived from their own local data and use them as the ground truth. The proposed algorithms can deal with an arbitrary number of Byzantine attackers and are provably convergent. Simulation results based on a real-world dataset are presented to verify the theoretical results and demonstrate the effectiveness of the proposed algorithms.

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points.

Are you implementing a machine learning algorithm at the moment? Implementing algorithms from scratch is one of the biggest mistakes I see beginners make. Don't Implement Machine Learning Algorithms Photo by kirandulo, some rights reserved. Here's a snippet of an email I received: Why do I have to implement algorithms from scratch? It seems that a lot of developers get caught in this challenge.

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In this paper, we propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. We use the general framework of Bregman distance functions to compute the proximal maps. Our method not only allows using two different extrapolation points to evaluate gradients and adding the inertial force, but also takes advantage of randomly picking the block of variables to update. Moreover, our method does not require a restarting step, and as such, it is not a monotonically decreasing method. To prove the convergence of the whole generated sequence to a critical point, we modify the convergence proof recipe of Bolte, Sabach and Teboulle (Proximal alternating linearized minimization for non-convex and non-smooth problems, Math. Prog. 146(1):459--494, 2014), and combine it with auxiliary functions. We deploy the proposed methods to solve non-negative matrix factorization (NMF) problems and show that they compete favourably with the state-of-the-art NMF algorithms.

The field of few-shot learning has been laboriously explored in the supervised setting, where per-class labels are available. On the other hand, the unsupervised few-shot learning setting, where no labels of any kind are required, has seen little investigation. We propose a method, named Assume, Augment and Learn or AAL, for generating few-shot tasks using unlabeled data. We randomly label a random subset of images from an unlabeled dataset to generate a support set. Then by applying data augmentation on the support set's images, and reusing the support set's labels, we obtain a target set. The resulting few-shot tasks can be used to train any standard meta-learning framework. Once trained, such a model, can be directly applied on small real-labeled datasets without any changes or fine-tuning required. In our experiments, the learned models achieve good generalization performance in a variety of established few-shot learning tasks on Omniglot and Mini-Imagenet.

Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like robust estimators using similar techniques that optimize GANs. In this paper, we introduce a general learning via classification framework based on the notion of proper scoring rules. This framework allows us to understand both matrix depth function and various GANs through the lens of variational approximations of $f$-divergences induced by proper scoring rules. We then propose a new class of robust scatter estimators in this framework by carefully constructing discriminators with appropriate neural network structures. These estimators are proved to achieve the minimax rate of scatter estimation under Huber's contamination model. Our numerical results demonstrate its good performance under various settings against competitors in the literature.

Learning with noisy labels, which aims to reduce expensive labors on accurate annotations, has become imperative in the Big Data era. Previous noise transition based method has achieved promising results and presented a theoretical guarantee on performance in the case of class-conditional noise. However, this type of approaches critically depend on an accurate pre-estimation of the noise transition, which is usually impractical. Subsequent improvement adapts the pre-estimation along with the training progress via a Softmax layer. However, the parameters in the Softmax layer are highly tweaked for the fragile performance due to the ill-posed stochastic approximation. To address these issues, we propose a Latent Class-Conditional Noise model (LCCN) that naturally embeds the noise transition under a Bayesian framework. By projecting the noise transition into a Dirichlet-distributed space, the learning is constrained on a simplex based on the whole dataset, instead of some ad-hoc parametric space. We then deduce a dynamic label regression method for LCCN to iteratively infer the latent labels, to stochastically train the classifier and to model the noise. Our approach safeguards the bounded update of the noise transition, which avoids previous arbitrarily tuning via a batch of samples. We further generalize LCCN for open-set noisy labels and the semi-supervised setting. We perform extensive experiments with the controllable noise data sets, CIFAR-10 and CIFAR-100, and the agnostic noise data sets, Clothing1M and WebVision17. The experimental results have demonstrated that the proposed model outperforms several state-of-the-art methods.