Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability distribution for the interventional distribution resulting from the action. In many cases an identifiability algorithm may return a complicated expression that contains variables that are in fact unnecessary. In practice this can lead to additional computational burden and increased bias or inefficiency of estimates when dealing with measurement error or missing data. We present graphical criteria to detect variables which are redundant in identifying causal effects. We also provide an improved version of a well-known identifiability algorithm that implements these criteria.

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant extension of the "anchored regression" method formulated and analyzed in [9] for regression with convex non-linearities. Our main assumption, in addition to other mild statistical and computational assumptions, is availability of a certain approximation oracle for the average of the gradients of the observation functions at a ground truth. Under this assumption and using a PAC-Bayesian analysis we show that the proposed estimator produces an accurate estimate with high probability. As a concrete example, we study the proposed framework in the bilinear regression problem with Gaussian factors and quantify a sufficient sample complexity for exact recovery. Furthermore, we describe a computationally tractable scheme that provably produces the required approximation oracle in the considered bilinear regression problem.

One of the big restrictions in brain computer interface field is the very limited training samples, it is difficult to build a reliable and usable system with such limited data. Inspired by generative adversarial networks, we propose a conditional Deep Convolutional Generative Adversarial (cDCGAN) Networks method to generate more artificial EEG signal automatically for data augmentation to improve the performance of convolutional neural networks in brain computer interface field and overcome the small training dataset problems. We evaluate the proposed cDCGAN method on BCI competition dataset of motor imagery. The results show that the generated artificial EEG data from Gaussian noise can learn the features from raw EEG data and has no less than the classification accuracy of raw EEG data in the testing dataset. Also by using generated artificial data can effectively improve classification accuracy at the same model with limited training data.

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high-dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterpart, we propose a new regularization method that leverages the clustered nature of data that is often encountered in practice. Our theoretical results indicate that this method overcomes the curse of dimensionality. This theoretical guarantee is supported by numerical experiments on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data.

It is well known that, for most datasets, the use of large-size minibatches for Stochastic Gradient Descent (SGD) typically leads to slow convergence and poor generalization. On the other hand, large minibatches are of great practical interest as they allow for a better exploitation of modern GPUs. Previous literature on the subject concentrated on how to adjust the main SGD parameters (in particular, the learning rate) when using large minibatches. In this work we introduce an additional feature, that we call minibatch persistency, that consists in reusing the same minibatch for K consecutive SGD iterations. The computational conjecture here is that a large minibatch contains a significant sample of the training set, so one can afford to slightly overfitting it without worsening generalization too much. The approach is intended to speedup SGD convergence, and also has the advantage of reducing the overhead related to data loading on the internal GPU memory. We present computational results on CIFAR-10 with an AlexNet architecture, showing that even small persistency values (K=2 or 5) already lead to a significantly faster convergence and to a comparable (or even better) generalization than the standard "disposable minibatch" approach (K=1), in particular when large minibatches are used. The lesson learned is that minibatch persistency can be a simple yet effective way to deal with large minibatches.

We consider time-domain digital backpropagation with chromatic dispersion filters jointly optimized and quantized using machine-learning techniques. Compared to the baseline implementations, we show improved BER performance and 40% power dissipation reductions in 28-nm CMOS. Joint Filter Optimization using Deep Learning The system setup is shown in Figure 1, where the four quantization blocks can be ignored for now. Introduction Fiber nonlinearities impose a fundamental limitation on transmission performance and various nonlinear compensation schemes have been proposed. Our focus is on digital backpropagation (DBP) which emulates backward fiber propagation using digital signal processing (DSP).

Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb's rule and the contrastive divergence algorithm. It operates in two phases, the forward (or free) phase, where the data are fed to the network, and a backward (or clamped) phase, where the target signals are clamped to the output layer of the network and the feedback signals are transformed through the transpose synaptic weight matrices. This implies symmetries at the synaptic level, for which there is no evidence in the brain. In this work, we propose a new variant of the algorithm, called random contrastive Hebbian learning, which does not rely on any synaptic weights symmetries. Instead, it uses random matrices to transform the feedback signals during the clamped phase, and the neural dynamics are described by first order non-linear differential equations. The algorithm is experimentally verified by solving a Boolean logic task, classification tasks (handwritten digits and letters), and an autoencoding task. This article also shows how the parameters affect learning, especially the random matrices. We use the pseudospectra analysis to investigate further how random matrices impact the learning process. Finally, we discuss the biological plausibility of the proposed algorithm, and how it can give rise to better computational models for learning.

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, which captures key structural elements in the resulting embedding space. However, to date, there has been little work exploring exactly which topological structures are being learned in the embeddings process. In this paper, we investigate if graph embeddings are approximating something analogous with traditional vertex level graph features. If such a relationship can be found, it could be used to provide a theoretical insight into how graph embedding approaches function. We perform this investigation by predicting known topological features, using supervised and unsupervised methods, directly from the embedding space. If a mapping between the embeddings and topological features can be found, then we argue that the structural information encapsulated by the features is represented in the embedding space. To explore this, we present extensive experimental evaluation from five state-of-the-art unsupervised graph embedding techniques, across a range of empirical graph datasets, measuring a selection of topological features. We demonstrate that several topological features are indeed being approximated by the embedding space, allowing key insight into how graph embeddings create good representations.

Predictive process monitoring is concerned with the analysis of events produced during the execution of a process in order to predict the future state of ongoing cases thereof. Existing techniques in this field are able to predict, at each step of a case, the likelihood that the case will end up in an undesired outcome. These techniques, however, do not take into account what process workers may do with the generated predictions in order to decrease the likelihood of undesired outcomes. This paper proposes a framework for prescriptive process monitoring, which extends predictive process monitoring approaches with the concepts of alarms, interventions, compensations, and mitigation effects. The framework incorporates a parameterized cost model to assess the cost-benefit tradeoffs of applying prescriptive process monitoring in a given setting. The paper also outlines an approach to optimize the generation of alarms given a dataset and a set of cost model parameters. The proposed approach is empirically evaluated using a range of real-life event logs.

The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations of CP on standard Knowledge Base Completion benchmarks are lagging behind their competitors. In this work, we attempt to understand the limits of CP for knowledge base completion. First, we motivate and test a novel regularizer, based on tensor nuclear $p$-norms. Then, we present a reformulation of the problem that makes it invariant to arbitrary choices in the inclusion of predicates or their reciprocals in the dataset. These two methods combined allow us to beat the current state of the art on several datasets with a CP decomposition, and obtain even better results using the more advanced ComplEx model.