In this paper we consider how to evaluate survival distribution predictions with measures of discrimination. This is a non-trivial problem as discrimination measures are the most commonly used in survival analysis and yet there is no clear method to derive a risk prediction from a distribution prediction. We survey methods proposed in literature and software and consider their respective advantages and disadvantages. Whilst distributions are frequently evaluated by discrimination measures, we find that the method for doing so is rarely described in the literature and often leads to unfair comparisons. We find that the most robust method of reducing a distribution to a risk is to sum over the predicted cumulative hazard. We recommend that machine learning survival analysis software implements clear transformations between distribution and risk predictions in order to allow more transparent and accessible model evaluation.

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical behavior can be fundamental in learning theory. Despite significant progress in characterizing its statistical property, the majority of the results are based on the assumption that samples are independent and identical distributed (i.i.d.), which is too restrictive for real-world applications. This paper concerns the statistical property of regularized modal regression (RMR) within an important dependence structure - Markov dependent. Specifically, we establish the upper bound for RMR estimator under moderate conditions and give an explicit learning rate. Our results show that the Markov dependence impacts on the generalization error in the way that sample size would be discounted by a multiplicative factor depending on the spectral gap of underlying Markov chain. This result shed a new light on characterizing the theoretical underpinning for robust regression.

A law of large numbers for the empirical distribution of parameters of a one-layer artificial neural networks with sparse connectivity is derived for a simultaneously increasing number of both, neurons and training iterations of the stochastic gradient descent.

Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes with gradient noise, often leading to specific step size and momentum choices in order to guarantee convergence, set aside acceleration. Proximal point methods, on the other hand, have gained much attention due to their numerical stability and elasticity against imperfect tuning. Their stochastic accelerated variants though have received limited attention: how momentum interacts with the stability of (stochastic) proximal point methods remains largely unstudied. To address this, we focus on the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM), and show that SPPAM allows a faster linear convergence to a neighborhood compared to stochastic proximal point algorithm (SPPA) with a better contraction factor, under proper hyperparameter tuning. In terms of stability, we show that SPPAM depends on problem constants more favorably than SGDM, allowing a wider range of step size and momentum that lead to convergence.

For personalized ranking models, the well-calibrated probability of an item being preferred by a user has great practical value. While existing work shows promising results in image classification, probability calibration has not been much explored for personalized ranking. In this paper, we aim to estimate the calibrated probability of how likely a user will prefer an item. We investigate various parametric distributions and propose two parametric calibration methods, namely Gaussian calibration and Gamma calibration. Each proposed method can be seen as a post-processing function that maps the ranking scores of pre-trained models to well-calibrated preference probabilities, without affecting the recommendation performance. We also design the unbiased empirical risk minimization framework that guides the calibration methods to learning of true preference probability from the biased user-item interaction dataset. Extensive evaluations with various personalized ranking models on real-world datasets show that both the proposed calibration methods and the unbiased empirical risk minimization significantly improve the calibration performance.

In this paper, we make the very first attempt to investigate the integration of deep hash learning with vehicle re-identification. We propose a deep hash-based vehicle re-identification framework, dubbed DVHN, which substantially reduces memory usage and promotes retrieval efficiency while reserving nearest neighbor search accuracy. Concretely,~DVHN directly learns discrete compact binary hash codes for each image by jointly optimizing the feature learning network and the hash code generating module. Specifically, we directly constrain the output from the convolutional neural network to be discrete binary codes and ensure the learned binary codes are optimal for classification. To optimize the deep discrete hashing framework, we further propose an alternating minimization method for learning binary similarity-preserved hashing codes. Extensive experiments on two widely-studied vehicle re-identification datasets- \textbf{VehicleID} and \textbf{VeRi}-~have demonstrated the superiority of our method against the state-of-the-art deep hash methods. \textbf{DVHN} of $2048$ bits can achieve 13.94\% and 10.21\% accuracy improvement in terms of \textbf{mAP} and \textbf{Rank@1} for \textbf{VehicleID (800)} dataset. For \textbf{VeRi}, we achieve 35.45\% and 32.72\% performance gains for \textbf{Rank@1} and \textbf{mAP}, respectively.

Graph representation learning (GRL) on attribute-missing graphs, which is a common yet challenging problem, has recently attracted considerable attention. We observe that existing literature: 1) isolates the learning of attribute and structure embedding thus fails to take full advantages of the two types of information; 2) imposes too strict distribution assumption on the latent space variables, leading to less discriminative feature representations. In this paper, based on the idea of introducing intimate information interaction between the two information sources, we propose our Siamese Attribute-missing Graph Auto-encoder (SAGA). Specifically, three strategies have been conducted. First, we entangle the attribute embedding and structure embedding by introducing a siamese network structure to share the parameters learned by both processes, which allows the network training to benefit from more abundant and diverse information. Second, we introduce a K-nearest neighbor (KNN) and structural constraint enhanced learning mechanism to improve the quality of latent features of the missing attributes by filtering unreliable connections. Third, we manually mask the connections on multiple adjacent matrices and force the structural information embedding sub-network to recover the true adjacent matrix, thus enforcing the resulting network to be able to selectively exploit more high-order discriminative features for data completion. Extensive experiments on six benchmark datasets demonstrate the superiority of our SAGA against the state-of-the-art methods.

While the fuel economy of new gasoline or diesel-powered vehicles improves every year, green vehicles are considered even more environmentally friendly because they're powered by alternative fuel or electricity. Hybrid electric vehicles (HEVs), battery only electric vehicles (BEVs), fuel cell electric vehicles (FCEVs), hydrogen cars, and solar cars are all considered types of green vehicles. Charging stations for green vehicles are similar to the gas pump in a gas station. They can be fixed on the ground or wall and installed in public buildings (shopping malls, public parking lots, and so on), residential district parking lots, or charging stations. They can be based on different voltage levels and charge various types of electric vehicles.

Most stock trading algorithms that incorporate machine learning are based upon some form of linear regression. There are benefits and drawbacks to this method. The benefit of this is that the predicted prices of linear regression can be integrated into more complex values, that need the actual price values to function. The drawback is that for the basic "buy low, sell high" strategy, it is not directly related to predicting the direction of the price. What would happen if we used logistic regression, or more specifically binary classification, to predict if the price will increase or decrease? Theoretically, it would hone in on direction itself, and become more accurate than the signals generated by linear regression.

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs. Furthermore, the online computational efficiency improves by approximately 100 times compared with the conventional KPCA. With the Tennessee Eastman (TE) process benchmark, the effectiveness and superiority of the proposed method is illustrated.