Many data generating processes involve latent random variables over discrete combinatorial spaces whose size grows factorially with the dataset. In these settings, existing posterior inference methods can be inaccurate and/or very slow. In this work we develop methods for efficient amortized approximate Bayesian inference over discrete combinatorial spaces, with applications to random permutations, probabilistic clustering (such as Dirichlet process mixture models) and random communities (such as stochastic block models). The approach is based on mapping distributed, symmetry-invariant representations of discrete arrangements into conditional probabilities. The resulting algorithms parallelize easily, yield iid samples from the approximate posteriors, and can easily be applied to both conjugate and non-conjugate models, as training only requires samples from the generative model.

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy. Both could seriously limit applicability of deep learning in some domains particularly involving predictions of continuous variables with a small size of samples. Inspired by residual convolutional neural network in computer vision and recent findings of crucial shortcuts in the brains in neuroscience, we propose an autoencoder-based residual deep network for robust prediction. In a nested way, we leverage shortcut connections to implement residual mapping with a balanced structure for efficient propagation of error signals. The novel method is demonstrated by multiple datasets, imputation of high spatiotemporal resolution non-randomness missing values of aerosol optical depth, and spatiotemporal estimation of fine particulate matter <2.5 \mu m, achieving the cutting edge of accuracy and efficiency. Our approach is also a general-purpose regression learner to be applicable in diverse domains.

The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software package, an easy-to-use, high-performance Python implementation of the scattering transform in 1D, 2D, and 3D that is compatible with modern deep learning frameworks. All transforms may be executed on a GPU (in addition to CPU), offering a considerable speed up over CPU implementations. The package also has a small memory footprint, resulting inefficient memory usage. The source code, documentation, and examples are available undera BSD license at https://www.kymat.io/

Diffusion MRI is the modality of choice to study alterations of white matter. In the past years, various works have used diffusion MRI for automatic classification of Alzheimers disease. However, the performances obtained with different approaches are difficult to compare because of variations in components such as input data, participant selection, image preprocessing, feature extraction, feature selection (FS) and cross-validation (CV) procedure. Moreover, these studies are also difficult to reproduce because these different components are not readily available. In a previous work (Samper-Gonzalez et al. 2018), we proposed an open-source framework for the reproducible evaluation of AD classification from T1-weighted (T1w) MRI and PET data. In the present paper, we extend this framework to diffusion MRI data. The framework comprises: tools to automatically convert ADNI data into the BIDS standard, pipelines for image preprocessing and feature extraction, baseline classifiers and a rigorous CV procedure. We demonstrate the use of the framework through assessing the influence of diffusion tensor imaging (DTI) metrics (fractional anisotropy - FA, mean diffusivity - MD), feature types, imaging modalities (diffusion MRI or T1w MRI), data imbalance and FS bias. First, voxel-wise features generally gave better performances than regional features. Secondly, FA and MD provided comparable results for voxel-wise features. Thirdly, T1w MRI performed better than diffusion MRI. Fourthly, we demonstrated that using non-nested validation of FS leads to unreliable and over-optimistic results. All the code is publicly available: general-purpose tools have been integrated into the Clinica software (www.clinica.run) and the paper-specific code is available at: https://gitlab.icm-institute.org/aramislab/AD-ML.

Value functions derived from Markov decision processes arise as a central component of algorithms as well as performance metrics in many statistics and engineering applications of machine learning techniques. Computation of the solution to the associated Bellman equations is challenging in most practical cases of interest. A popular class of approximation techniques, known as Temporal Difference (TD) learning algorithms, are an important sub-class of general reinforcement learning methods. The algorithms introduced in this paper are intended to resolve two well-known difficulties of TD-learning approaches: Their slow convergence due to very high variance, and the fact that, for the problem of computing the relative value function, consistent algorithms exist only in special cases. First we show that the gradients of these value functions admit a representation that lends itself to algorithm design. Based on this result, a new class of differential TD-learning algorithms is introduced. For Markovian models on Euclidean space with smooth dynamics, the algorithms are shown to be consistent under general conditions. Numerical results show dramatic variance reduction when compared to standard methods.

Recently, the application of deep neural networks [1] has led to a phenomenal success in various artificial intelligence areas, e.g., computer vision, natural language processing, and audio recognition. However, the theoretical understanding of neural networks is still limited. One of the main difficulties of analyzing neural networks is the non-convexity of the objective function, which may cause many local minima. In practice, it is observed that when the number of parameters is sufficiently large, common optimization algorithmssuch as stochastic gradient descent (SGD) can achieve small training error [2-6]. These observations are often explained by the intuition that more parameters can smooth the landscape [4,7]. Among various definitions of over-parameterization, a popular one is that the last hidden layer has more neurons than the number of training samples. Even under this assumption, it is yet unclear to what extent we can prove a rigorous result. For instance, can we prove that for any neuron activation function, every local minimum is a global minimum? If not, what exactly can we prove, and what can we not prove?

Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider diffusion episodes as sequences of infections via recurrent neural models. In this paper we propose a model at the crossroads of these two extremes, which embeds the history of diffusion in infected nodes as hidden continuous states. Depending on the trajectory followed by the content before reaching a given node, the distribution of influence probabilities may vary. However, content trajectories are usually hidden in the data, which induces challenging learning problems. We propose a topological recurrent neural model which exhibits good experimental performances for diffusion modelling and prediction.

Abstract--Deep Neural Networks have achieved huge success at a wide spectrum of applications from language modeling, computer vision to speech recognition. However, nowadays, good performance alone is not sufficient to satisfy the needs of practical deployment where interpretability is demanded for cases involving ethicsand mission critical applications. The complex models of Deep Neural Networks make it hard to understand and reason the predictions, which hinders its further progress. To tackle this problem, we apply the Knowledge Distillation technique to distill Deep Neural Networks into decision trees in order to attain good performance and interpretability simultaneously. We formulate the problem at hand as a multi-output regression problem and the experiments demonstrate that the student model achieves significantly better accuracy performance (about 1% to 5%) than vanilla decision trees at the same level of tree depth. The experiments are implemented on the TensorFlow platform to make it scalable to big datasets. To the best of our knowledge, we are the first to distill Deep Neural Networks into vanilla decision trees on multi-class datasets. I. INTRODUCTION Despite Deep Neural Networks' (DNN) superior discrimination powerin many fields, the logics of each hidden feature representations before the output layer still remain to be blackbox. Understandingwhy a specific prediction is made is of utmost importance for the end-users to trust and adopt the model, and for the system designers to refine the model by performing feature engineering and parameter tuning.

We contribute a pop-song automation framework for lead melody generation and accompaniment arrangement. The framework reflects the major procedures of human music composition, generating both lead melody and piano accompaniment by a unified strategy. Specifically, we take chord progression as an input and propose three models to generate a structured melody with piano accompaniment textures. First, the harmony alternation model transforms a raw input chord progression to an altered one to better fit the specified music style. Second, the melody generation model generates the lead melody and other voices (melody lines) of the accompaniment using seasonal ARMA (Autoregressive Moving Average) processes. Third, the melody integration model integrates melody lines (voices) together as the final piano accompaniment. We evaluate the proposed framework using subjective listening tests. Experimental results show that the generated melodies are rated significantly higher than the ones generated by bi-directional LSTM, and our accompaniment arrangement result is comparable with a state-of-the-art commercial software, Band in a Box.

Emergent and unscheduled cardiology admissions from cardiac catheterization laboratory add complexity to the management of Cardiology and in-patient department. In this article, we sought to study the behavior of cardiology admissions from Catheterization laboratory using time series models. Our research involves retrospective cardiology admission data from March 1, 2012, to November 3, 2016, retrieved from a hospital in Iowa. Autoregressive integrated moving average (ARIMA), Holts method, mean method, na\"ive method, seasonal na\"ive, exponential smoothing, and drift method were implemented to forecast weekly cardiology admissions from Catheterization laboratory. ARIMA (2,0,2) (1,1,1) was selected as the best fit model with the minimum sum of error, Akaike information criterion and Schwartz Bayesian criterion. The model failed to reject the null hypothesis of stationarity, it lacked the evidence of independence, and rejected the null hypothesis of normality. The implication of this study will not only improve catheterization laboratory staff schedule, advocate efficient use of imaging equipment and inpatient telemetry beds but also equip management to proactively tackle inpatient overcrowding, plan for physical capacity expansion and so forth.