Large-batch stochastic gradient descent (SGD) is widely used for training in distributed deep learning because of its training-time efficiency, however, extremely large-batch SGD leads to poor generalization and easily converges to sharp minima, which prevents naive large-scale data-parallel SGD (DP-SGD) from converging to good minima. To overcome this difficulty, we propose gradient noise convolution (GNC), which effectively smooths sharper minima of the loss function. For DP-SGD, GNC utilizes so-called gradient noise, which is induced by stochastic gradient variation and convolved to the loss function as a smoothing effect. GNC computation can be performed by simply computing the stochastic gradient on each parallel worker and merging them, and is therefore extremely easy to implement. Due to convolving with the gradient noise, which tends to spread along a sharper direction of the loss function, GNC can effectively smooth sharp minima and achieve better generalization, whereas isotropic random noise cannot. We empirically show this effect by comparing GNC with isotropic random noise, and show that it achieves state-of-the-art generalization performance for large-scale deep neural network optimization.

Accurate models of patient survival probabilities provide important information to clinicians prescribing care for life-threatening and terminal ailments. A recently developed class of models - known as individual survival distributions (ISDs) - produces patient-specific survival functions that offer greater descriptive power of patient outcomes than was previously possible. Unfortunately, at the time of writing, ISD models almost universally lack uncertainty quantification. In this paper, we demonstrate that an existing method for estimating simultaneous prediction intervals from samples can easily be adapted for patient-specific survival curve analysis and yields accurate results. Furthermore, we introduce both a modification to the existing method and a novel method for estimating simultaneous prediction intervals and show that they offer competitive performance. It is worth emphasizing that these methods are not limited to survival analysis and can be applied in any context in which sampling the distribution of interest is tractable. Code is available at https://github.com/ssokota/spie .

Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often insufficient for visualizing the global and local structure of the data. In this paper, we present DIG (Dynamical Information Geometry), a visualization method for multivariate time series data that extracts an information geometry from a diffusion framework. Specifically, we implement a novel group of distances in the context of diffusion operators, which may be useful to reveal structure in the data that may not be accessible by the commonly used diffusion distances. Finally, we present a case study applying our visualization tool to EEG data to visualize sleep stages.

Two important topics in deep learning both involve incorporating humans into the modeling process: Model priors transfer information from humans to a model by constraining the model's parameters; Model attributions transfer information from a model to humans by explaining the model's behavior. We propose connecting these topics with attribution priors (https://github.com/suinleelab/attributionpriors), which allow humans to use the common language of attributions to enforce prior expectations about a model's behavior during training. We develop a differentiable axiomatic feature attribution method called expected gradients and show how to directly regularize these attributions during training. We demonstrate the broad applicability of attribution priors ($\Omega$) by presenting three distinct examples that regularize models to behave more intuitively in three different domains: 1) on image data, $\Omega_{\textrm{pixel}}$ encourages models to have piecewise smooth attribution maps; 2) on gene expression data, $\Omega_{\textrm{graph}}$ encourages models to treat functionally related genes similarly; 3) on a health care dataset, $\Omega_{\textrm{sparse}}$ encourages models to rely on fewer features. In all three domains, attribution priors produce models with more intuitive behavior and better generalization performance by encoding constraints that would otherwise be very difficult to encode using standard model priors.

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies--the pathwise, score function, and measure-valued gradient estimators-- exploring their historical developments, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.

In this paper we propose a fusion approach to continuous emotion recognition that combines visual and auditory modalities in their representation spaces to predict the arousal and valence levels. The proposed approach employs a pre-trained convolution neural network and transfer learning to extract features from video frames that capture the emotional content. For the auditory content, a minimalistic set of parameters such as prosodic, excitation, vocal tract, and spectral descriptors are used as features. The fusion of these two modalities is carried out at a feature level, before training a single support vector regressor (SVR) or at a prediction level, after training one SVR for each modality. The proposed approach also includes preprocessing and post-processing techniques which contribute favorably to improving the concordance correlation coefficient (CCC). Experimental results for predicting spontaneous and natural emotions on the RECOLA dataset have shown that the proposed approach takes advantage of the complementary information of visual and auditory modalities and provides CCCs of 0.749 and 0.565 for arousal and valence, respectively.

When forecasting time series with a hierarchical structure, the existing state of the art is to forecast each time series independently, and, in a post-treatment step, to reconcile the time series in a way that respects the hierarchy (Hyndman et al., 2011; Wickramasuriya et al., 2018). We propose a new loss function that can be incorporated into any maximum likelihood objective with hierarchical data, resulting in reconciled estimates with confidence intervals that correctly account for additional uncertainty due to imperfect reconciliation. We evaluate our method using a non-linear model and synthetic data on a counterfactual forecasting problem, where we have access to the ground truth and contemporaneous covariates, and show that we largely improve over the existing state-of-the-art method.

Introduced by Breiman (2001), Random Forests (RF) is one of the algorithms of choice in many supervised learning applications. The appeal of these methods comes from their remarkable accuracy in a variety of tasks, the small number (or even the absence) of parameters to tune, their reasonable computational cost at training and prediction time, and their suitability in highdimensional settings. Most commonly used RF algorithms, such as the original random forest procedure (Breiman, 2001), extra-trees (Geurts et al., 2006), or conditional inference forest (Hothorn et al., 2010) are batch algorithms, that require the whole dataset to be available at once. Several online random forests variants have been proposed to overcome this issue and handle data that come sequentially. Utgoff (1989) was the first to extend Quinlan's ID3 batch decision tree algorithm (see Quinlan, 1986) to an online setting. Later on, Domingos and Hulten (2000) introduce Hoeffding Trees that can be easily updated: since observations are available sequentially, a cell is split when (i) enough observations have fallen into this cell, (ii) the best split in the cell is statistically relevant (a generic Hoeffding inequality being used to assess the quality of the best split). Since random forests are known to exhibit better empirical performances than individual decision trees, online random forests have been proposed (see, e.g., Saffari et al., 2009; Denil et al., 2013).

Statistical Learning is the process of estimating an unknown probabilistic input-output relationship of a system using a limited number of observations; and a statistical learning machine (SLM) is the machine that learned such a process. While their roots grow deeply in Probability Theory, SLMs are ubiquitous in the modern world. Automatic Target Recognition (ATR) in military applications, Computer Aided Diagnosis (CAD) in medical imaging, DNA microarrays in Genomics, Optical Character Recognition (OCR), Speech Recognition (SR), spam email filtering, stock market prediction, etc., are few examples and applications for SLM; diverse fields but one theory. The field of Statistical Learning can be decomposed to two basic subfields, Design and Assessment. Three main groups of specializations-namely statisticians, engineers, and computer scientists (ordered ascendingly by programming capabilities and descendingly by mathematical rigor)-exist on the venue of this field and each takes its elephant bite. Exaggerated rigorous analysis of statisticians sometimes deprives them from considering new ML techniques and methods that, yet, have no "complete" mathematical theory. On the other hand, immoderate add-hoc simulations of computer scientists sometimes derive them towards unjustified and immature results. A prudent approach is needed that has the enough flexibility to utilize simulations and trials and errors without sacrificing any rigor. If this prudent attitude is necessary for this field it is necessary, as well, in other fields of Engineering.

Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite system of agglomerative hierarchical clustering strategies based on generalized means, which go from single linkage to complete linkage, passing through arithmetic average linkage and other clustering methods yet unexplored such as geometric linkage and harmonic linkage. We compare the different clustering strategies in terms of cophenetic correlation, mean absolute error, and also tree balance and space distortion, two new measures proposed to describe hierarchical trees. Unlike the β-flexible clustering system, we show that the versatile linkage family is space-conserving.