Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way to efficiently construct them. For the stochastic optimization problems that dominate contemporary machine learning, however, this approach is not readily available. We propose an iterative algorithm inspired by classic iterative linear solvers that uses a probabilistic model to actively infer a pre-conditioner in situations where Hessian-projections can only be constructed with strong Gaussian noise. The algorithm is empirically demonstrated to efficiently construct effective pre-conditioners for stochastic gradient descent and its variants. Experiments on problems of comparably low dimensionality show improved convergence. In very high-dimensional problems, such as those encountered in deep learning, the pre-conditioner effectively becomes an automatic learning-rate adaptation scheme, which we also empirically show to work well.

We consider compressed sensing formulated as a minimization problem of nonconvex sparse penalties, Smoothly Clipped Absolute deviation (SCAD) and Minimax Concave Penalty (MCP). The nonconvexity of these penalties is controlled by nonconvexity parameters, and L1 penalty is contained as a limit with respect to these parameters. The analytically derived reconstruction limit overcomes that of L1 and the algorithmic limit in the Bayes-optimal setting, when the nonconvexity parameters have suitable values. For the practical usage, we apply the approximate message passing (AMP) to these nonconvex penalties. We show that the performance of AMP is considerably improved by controlling nonconvexity parameters.

Practically, we are often in the dilemma that the labeled data at hand are inadequate to train a reliable classifier, and more seriously, some of these labeled data may be mistakenly labeled due to the various human factors. Therefore, this paper proposes a novel semi-supervised learning paradigm that can handle both label insufficiency and label inaccuracy. To address label insufficiency, we use a graph to bridge the data points so that the label information can be propagated from the scarce labeled examples to unlabeled examples along the graph edges. To address label inaccuracy, Graph Trend Filtering (GTF) and Smooth Eigenbase Pursuit (SEP) are adopted to filter out the initial noisy labels. GTF penalizes the l_0 norm of label difference between connected examples in the graph and exhibits better local adaptivity than the traditional l_2 norm-based Laplacian smoother. SEP reconstructs the correct labels by emphasizing the leading eigenvectors of Laplacian matrix associated with small eigenvalues, as these eigenvectors reflect real label smoothness and carry rich class separation cues. We term our algorithm as `Semi-supervised learning under Inadequate and Incorrect Supervision' (SIIS). Thorough experimental results on image classification, text categorization, and speech recognition demonstrate that our SIIS is effective in label error correction, leading to superior performance to the state-of-the-art methods in the presence of label noise and label scarcity.

Kernel extreme learning machine (KELM) is a novel feedforward neural network, which is widely used in classification problems. To some extent, it solves the existing problems of the invalid nodes and the large computational complexity in ELM. However, the traditional KELM classifier usually has a low test accuracy when it faces multiclass classification problems. In order to solve the above problem, a new classifier, Mexican Hat wavelet KELM classifier, is proposed in this paper. The proposed classifier successfully improves the training accuracy and reduces the training time in the multiclass classification problems. Moreover, the validity of the Mexican Hat wavelet as a kernel function of ELM is rigorously proved. Experimental results on different data sets show that the performance of the proposed classifier is significantly superior to the compared classifiers.

Deep Reinforcement Learning has shown great success in a variety of control tasks. However, it is unclear how close we are to the vision of putting Deep RL into practice to solve real world problems. In particular, common practice in the field is to train policies on largely deterministic simulators and to evaluate algorithms through training performance alone, without a train/test distinction to ensure models generalise and are not overfitted. Moreover, it is not standard practice to check for generalisation under domain shift, although robustness to such system change between training and testing would be necessary for real-world Deep RL control, for example, in robotics. In this paper we study these issues by first characterising the sources of uncertainty that provide generalisation challenges in Deep RL. We then provide a new benchmark and thorough empirical evaluation of generalisation challenges for state of the art Deep RL methods. In particular, we show that, if generalisation is the goal, then common practice of evaluating algorithms based on their training performance leads to the wrong conclusions about algorithm choice. Finally, we evaluate several techniques for improving generalisation and draw conclusions about the most robust techniques to date.

Correctly evaluating defenses against adversarial examples has proven to be extremely difficult. Despite the significant amount of recent work attempting to design defenses that withstand adaptive attacks, few have succeeded; most papers that propose defenses are quickly shown to be incorrect. We believe a large contributing factor is the difficulty of performing security evaluations. In this paper, we discuss the methodological foundations, review commonly accepted best practices, and suggest new methods for evaluating defenses to adversarial examples. We hope that both researchers developing defenses as well as readers and reviewers who wish to understand the completeness of an evaluation consider our advice in order to avoid common pitfalls.

In this paper, we propose a novel {\em $e$-exponentiated} transformation, $0 \le e<1$, for loss functions. When the transformation is applied to a convex loss function, the transformed loss function become more robust to outliers. Using a novel generalization error bound, we have theoretically shown that the transformed loss function has a tighter bound for datasets corrupted by outliers. Our empirical observation shows that the accuracy obtained using the transformed loss function can be significantly better than the same obtained using the original loss function and comparable to that obtained by some other state of the art methods in the presence of label noise.

Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an extension of the correlated topic model, the context is generated from a mixture of latent topics, and the equation is generated by an RNN that depends on the latent topic activations. To experiment with this model, we create a corpus of 400K equation-context pairs extracted from a range of scientific articles from arXiv, and fit the model using a variational autoencoder approach. Experimental results show that this joint model significantly outperforms existing topic models and equation models for scientific texts. Moreover, we qualitatively show that the model effectively captures the relationship between topics and mathematics, enabling novel applications such as topic-aware equation generation, equation topic inference, and topic-aware alignment of mathematical symbols and words.

Saliency Map, the gradient of the score function with respect to the input, is the most basic technique for interpreting deep neural network decisions. However, saliency maps are often visually noisy. Although several hypotheses were proposed to account for this phenomenon, there are few works that provide rigorous analyses of noisy saliency maps. In this paper, we identify that noise occurs in saliency maps when irrelevant features pass through ReLU activation functions. Then we propose Rectified Gradient, a method that solves this problem through layer-wise thresholding during backpropagation. Experiments with neural networks trained on CIFAR-10 and ImageNet showed effectiveness of our method and its superiority to other attribution methods.

In this paper, we propose a data collaboration analysis method for distributed datasets. The proposed method is a centralized machine learning while training datasets and models remain distributed over some institutions. Recently, data became large and distributed with decreasing costs of data collection. If we can centralize these distributed datasets and analyse them as one dataset, we expect to obtain novel insight and achieve a higher prediction performance compared with individual analyses on each distributed dataset. However, it is generally difficult to centralize the original datasets due to their huge data size or regarding a privacy-preserving problem. To avoid these difficulties, we propose a data collaboration analysis method for distributed datasets without sharing the original datasets. The proposed method centralizes only intermediate representation constructed individually instead of the original dataset.