Unsupervised learning is about capturing dependencies between variables and is driven by the contrast between the probable vs. improbable configurations of these variables, often either via a generative model that only samples probable ones or with an energy function (unnormalized log-density) that is low for probable ones and high for improbable ones. Here, we consider learning both an energy function and an efficient approximate sampling mechanism. Whereas the discriminator in generative adversarial networks (GANs) learns to separate data and generator samples, introducing an entropy maximization regularizer on the generator can turn the interpretation of the critic into an energy function, which separates the training distribution from everything else, and thus can be used for tasks like anomaly or novelty detection. Then, we show how Markov Chain Monte Carlo can be done in the generator latent space whose samples can be mapped to data space, producing better samples. These samples are used for the negative phase gradient required to estimate the log-likelihood gradient of the data space energy function. To maximize entropy at the output of the generator, we take advantage of recently introduced neural estimators of mutual information. We find that in addition to producing a useful scoring function for anomaly detection, the resulting approach produces sharp samples while covering the modes well, leading to high Inception and Frechet scores.

This paper aims to explore models based on the extreme gradient boosting (XGBoost) approach for business risk classification. Feature selection (FS) algorithms and hyper-parameter optimizations are simultaneously considered during model training. The five most commonly used FS methods including weight by Gini, weight by Chi-square, hierarchical variable clustering, weight by correlation, and weight by information are applied to alleviate the effect of redundant features. Two hyper-parameter optimization approaches, random search (RS) and Bayesian tree-structured Parzen Estimator (TPE), are applied in XGBoost. The effect of different FS and hyper-parameter optimization methods on the model performance are investigated by the Wilcoxon Signed Rank Test. The performance of XGBoost is compared to the traditionally utilized logistic regression (LR) model in terms of classification accuracy, area under the curve (AUC), recall, and F1 score obtained from the 10-fold cross validation. Results show that hierarchical clustering is the optimal FS method for LR while weight by Chi-square achieves the best performance in XG-Boost. Both TPE and RS optimization in XGBoost outperform LR significantly. TPE optimization shows a superiority over RS since it results in a significantly higher accuracy and a marginally higher AUC, recall and F1 score. Furthermore, XGBoost with TPE tuning shows a lower variability than the RS method. Finally, the ranking of feature importance based on XGBoost enhances the model interpretation. Therefore, XGBoost with Bayesian TPE hyper-parameter optimization serves as an operative while powerful approach for business risk modeling.

Markov random fields (MRFs) find applications in a variety of machine learning areas, while the inference and learning of such models are challenging in general. In this paper, we propose the Adversarial Variational Inference and Learning (AVIL) algorithm to solve the problems with a minimal assumption about the model structure of an MRF. AVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function, respectively. The variational distributions, which are parameterized as neural networks, provide an estimate of the negative log likelihood of the MRF. On one hand, the estimate is in an intuitive form of approximate contrastive free energy. On the other hand, the estimate is a minimax optimization problem, which is solved by stochastic gradient descent in an alternating manner. We apply AVIL to various undirected generative models in a fully black-box manner and obtain better results than existing competitors on several real datasets.

As part of autonomous car driving systems, semantic segmentation is an essential component to obtain a full understanding of the car's environment. One difficulty, that occurs while training neural networks for this purpose, is class imbalance of training data. Consequently, a neural network trained on unbalanced data in combination with maximum a-posteriori classification may easily ignore classes that are rare in terms of their frequency in the dataset. However, these classes are often of highest interest. We approach such potential misclassifications by weighting the posterior class probabilities with the prior class probabilities which in our case are the inverse frequencies of the corresponding classes in the training dataset. More precisely, we adopt a localized method by computing the priors pixel-wise such that the impact can be analyzed at pixel level as well. In our experiments, we train one network from scratch using a proprietary dataset containing 20,000 annotated frames of video sequences recorded from street scenes. The evaluation on our test set shows an increase of average recall with regard to instances of pedestrians and info signs by $25\%$ and $23.4\%$, respectively. In addition, we significantly reduce the non-detection rate for instances of the same classes by $61\%$ and $38\%$.

Recovering pairwise interactions, i.e. pairs of input features whose joint effect on an output is different from the sum of their marginal effects, is central in many scientific applications. We conceptualize a solution to this problem as a two-stage procedure: first, we model the relationship between the features and the output using a flexible hybrid neural network; second, we detect feature interactions from the trained model. For the second step we propose a simple and intuitive interaction measure (IM), which has no specific requirements on the machine learning model used in the first step, only that it defines a mapping from an input to an output. And in a special case it reduces to the averaged Hessian of the input-output mapping. Importantly, our method upper bounds the interaction recovery error with the error of the learning model, which ensures that we can improve the recovered interactions by training a more accurate model. We present analyses of simulated and real-world data which demonstrate the benefits of our method compared to available alternatives, and theoretically analyse its properties and relation to other methods.

State-of-the-art neural networks are vulnerable to adversarial examples; they can easily misclassify inputs that are imperceptibly different than their training and test data. In this work, we establish that the use of cross-entropy loss function and the low-rank features of the training data have responsibility for the existence of these inputs. Based on this observation, we suggest that addressing adversarial examples requires rethinking the use of cross-entropy loss function and looking for an alternative that is more suited for minimization with low-rank features. In this direction, we present a training scheme called differential training, which uses a loss function defined on the differences between the features of points from opposite classes. We show that differential training can ensure a large margin between the decision boundary of the neural network and the points in the training dataset. This larger margin increases the amount of perturbation needed to flip the prediction of the classifier and makes it harder to find an adversarial example with small perturbations. We test differential training on a binary classification task with CIFAR-10 dataset and demonstrate that it radically reduces the ratio of images for which an adversarial example could be found -- not only in the training dataset, but in the test dataset as well.

We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or make strong assumptions about the form of the mixing matrix. Our algorithm does not make any sparsity assumption yet enjoys favorable computational and theoretical properties. Our algorithm consists of two main steps: (a) estimation of the Hessians of the cumulant generating function (as opposed to the fourth and higher order cumulants used by most algorithms) and (b) a novel semi-definite programming (SDP) relaxation for recovering a mixing component. We show that this relaxation can be efficiently solved with a projected accelerated gradient descent method, which makes the whole algorithm computationally practical. Moreover, we conjecture that the proposed program recovers a mixing component at the rate k < p^2/4 and prove that a mixing component can be recovered with high probability when k < (2 - epsilon) p log p when the original components are sampled uniformly at random on the hyper sphere. Experiments are provided on synthetic data and the CIFAR-10 dataset of real images.

Time series forecasting is a crucial component of many important applications, ranging from predicting thebehavior of financial markets [5], to accurate energy load prediction [13]. Even though the large amount of data that can be nowadays collected from these domains provide an unprecedented opportunity for applying powerful deep learning (DL) methods [23, 41, 24], the high-dimensionality, velocity and variety of such data also pose significant and unique challenges that must be carefully addressed for each application. To this end, many methods have been proposed to analyze and forecast time series data. For example, traditional approaches employ adaptive distance metrics, such as Dynamic Time Wrapping [4], to tackle these kind of tasks. However, with the advent of DL the interest is gradually shifting toward using neural network-based methods, including recurrent and convolutional architectures [25, 7], that seem to be more effective for handling such kind of data. It is worth noting that other approaches for time series analysis also exist, such as using the Bag-of-Features model (BoF) [35]. The BoF model was recently adapted toward efficiently processing large amounts of complex and high-dimensional time series [2, 1, 32], due its ability to analyze objects that consist of a varying number of features, as well as withstanding distribution shifts better than competitive methods [29]. The Bag-of-Features model (BoF) involves the following pipeline [35]: a) Several feature vectors are extracted from each input object, e.g., an image or time series. This step is called feature extraction and allows for forming the feature space, where each object is represented as a set of feature vectors.

In this survey paper, we systematically summarize the current literature on studies that apply machine learning (ML) and data mining techniques to bearing fault diagnostics. Conventional ML methods, including artificial neural network (ANN), principal component analysis (PCA), support vector machines (SVM), etc., have been successfully applied to detecting and categorizing bearing faults since the last decade, while the application of deep learning (DL) methods has sparked great interest in both the industry and academia in the last five years. In this paper, we will first review the conventional ML methods, before taking a deep dive into the latest developments in DL algorithms for bearing fault applications. Specifically, the superiority of the DL based methods over the conventional ML methods are analyzed in terms of metrics directly related to fault feature extraction and classifier performances; the new functionalities offered by DL techniques that cannot be accomplished before are also summarized. In addition, to obtain a more intuitive insight, a comparative study is performed on the classifier performance and accuracy for a number of papers utilizing the open source Case Western Reserve University (CWRU) bearing data set. Finally, based on the nature of the time-series 1-D data obtained from sensors monitoring the bearing conditions, recommendations and suggestions are provided to applying DL algorithms on bearing fault diagnostics based on specific applications, as well as future research directions to further improve its performance.

We consider deep classifying neural networks. We expose a structure in the derivative of the logits with respect to the parameters of the model, which is used to explain the existence of outliers in the spectrum of the Hessian. Previous works decomposed the Hessian into two components, attributing the outliers to one of them, the so-called Covariance of gradients. We show this term is not a Covariance but a second moment matrix, i.e., it is influenced by means of gradients. These means possess an additive two-way structure that is the source of the outliers in the spectrum. This structure can be used to approximate the principal subspace of the Hessian using certain "averaging" operations, avoiding the need for high-dimensional eigenanalysis. We corroborate this claim across different datasets, architectures and sample sizes.