Developing electrophysiological recordings of brain neuronal activity and their analysis provide a basis for exploring the structure of brain function and nervous system investigation. The recorded signals are typically a combination of spikes and noise. High amounts of background noise and possibility of electric signaling recording from several neurons adjacent to the recording site have led scientists to develop neuronal signal processing tools such as spike sorting to facilitate brain data analysis. Spike sorting plays a pivotal role in understanding the electrophysiological activity of neuronal networks. This process prepares recorded data for interpretations of neurons interactions and understanding the overall structure of brain functions. Spike sorting consists of three steps: spike detection, feature extraction, and spike clustering. There are several methods to implement each of spike sorting steps. This paper provides a systematic comparison of various spike sorting sub-techniques applied to real extracellularly recorded data from a rat brain basolateral amygdala. An efficient sorted data resulted from careful choice of spike sorting sub-methods leads to better interpretation of the brain structures connectivity under different conditions, which is a very sensitive concept in diagnosis and treatment of neurological disorders. Here, spike detection is performed by appropriate choice of threshold level via three different approaches. Feature extraction is done through PCA and Kernel PCA methods, which Kernel PCA outperforms. We have applied four different algorithms for spike clustering including K-means, Fuzzy C-means, Bayesian and Fuzzy maximum likelihood estimation. As one requirement of most clustering algorithms, optimal number of clusters is achieved through validity indices for each method. Finally, the sorting results are evaluated using inter-spike interval histograms.

Two types of zeroth-order stochastic algorithms have recently been designed for nonconvex optimization respectively based on the first-order techniques SVRG and SARAH/SPIDER. This paper addresses several important issues that are still open in these methods. First, all existing SVRG-type zeroth-order algorithms suffer from worse function query complexities than either zeroth-order gradient descent (ZO-GD) or stochastic gradient descent (ZO-SGD). In this paper, we propose a new algorithm ZO-SVRG-Coord-Rand and develop a new analysis for an existing ZO-SVRG-Coord algorithm proposed in Liu et al. 2018b, and show that both ZO-SVRG-Coord-Rand and ZO-SVRG-Coord (under our new analysis) outperform other exiting SVRG-type zeroth-order methods as well as ZO-GD and ZO-SGD. Second, the existing SPIDER-type algorithm SPIDER-SZO (Fang et al. 2018) has superior theoretical performance, but suffers from the generation of a large number of Gaussian random variables as well as a $\sqrt{\epsilon}$-level stepsize in practice. In this paper, we develop a new algorithm ZO-SPIDER-Coord, which is free from Gaussian variable generation and allows a large constant stepsize while maintaining the same convergence rate and query complexity, and we further show that ZO-SPIDER-Coord automatically achieves a linear convergence rate as the iterate enters into a local PL region without restart and algorithmic modification.

State-of-art deep neural networks (DNN) are vulnerable to attacks by adversarial examples: a carefully designed small perturbation to the input, that is imperceptible to human, can mislead DNN. To understand the root cause of adversarial examples, we quantify the probability of adversarial example existence for linear classifiers. Previous mathematical definition of adversarial examples only involves the overall perturbation amount, and we propose a more practical relevant definition of strong adversarial examples that separately limits the perturbation along the signal direction also. We show that linear classifiers can be made robust to strong adversarial examples attack in cases where no adversarial robust linear classifiers exist under the previous definition. The quantitative formulas are confirmed by numerical experiments using a linear support vector machine (SVM) classifier. The results suggest that designing general strong-adversarial-robust learning systems is feasible but only through incorporating human knowledge of the underlying classification problem.

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few nonuniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI. The slow nature of signal acquisition in magnetic resonance imaging (MRI), where the image is formed from a sequence of Fourier samples, often restricts the achievable spatial and temporal resolution in multidimensional static and dynamic imaging applications. Discrete compressed sensing (CS) methods provided a major breakthrough to accelerate the magnetic resonance (MR) signal acquisition by reducing the sampling burden. As described in an introductory article in this special issue [1] these algorithms exploited the sparsity of the discrete signal in a transform domain to recover the images from a few measurements. In this paper, we review a continuous domain extension of CS using a structured low-rank (SLR) framework for the recovery of an image or a series of images from a few measurements using various compactness assumptions [2]-[22]. The general strategy of the SLR framework starts with defining a lifting operation to construct a structured matrix, whose entries are functions of the signal samples. The SLR algorithms exploit the dual relationships between the signal compactness properties (e.g. This dual relationship allows recovery of the signal from a few samples in the measurement domain as an SLR optimization problem. MJ and MM are with the University of Iowa, Iowa City, IA 52242 (emails: mathews-jacob@uiowa.edu,merry-mani@uiowa.edu). JCY is with the Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea (email: jong.ye@kaist.ac.kr).

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive performance, the techniques have a limited capability to incorporate the uncertainty in the underlined graph structure. In order to address this issue, a Bayesian GCNN (BGCN) framework was recently proposed. In this framework, the observed graph is considered to be a random realization from a parametric random graph model and the joint Bayesian inference of the graph and GCNN weights is performed. In this paper, we propose a non-parametric generative model for graphs and incorporate it within the BGCN framework. In addition to the observed graph, our approach effectively uses the node features and training labels in the posterior inference of graphs and attains superior or comparable performance in benchmark node classification tasks.

Such 2D representations have lower dimensionality than audio waveforms and they easily fit advanced deep learning architectures mainly developed for computer visi on applications. Mel frequency cepstral coefficient (MFCC), short-time Fourier transformation (STFT), discrete wavel et transformation (DWT) are among the most pervasive 2D signal representations which essentially visualize frequ ency-magnitude distribution of a given reconstructed signal ove r time. Thus far, the best sound classification accuracy has been achieved for deep learning algorithms trained on 2D signal representations [1, 2]. However, it has been shown th at despite achieving high performance, the approaches based on 2D representations are very vulnerable against adversar ial attacks [3]. Unfortunately, this poses a strict security is sue because crafted adversarial examples not only mislead the target model toward a wrong label, but also, they are transfe r-able to other models including conventional algorithms suc h as support vector machines (SVM) [3].

Multidimensional data have become ubiquitous and are frequently involved in situations where the information is aggregated over multiple data atoms. The aggregation can be over time or other features, such as geographical location or group affiliation. We often have access to multiple aggregated views of the same data, each aggregated in one or more dimensions, especially when data are collected or measured by different agencies. However, data mining and machine learning models require detailed data for personalized analysis and prediction. Thus, data disaggregation algorithms are becoming increasingly important in various domains. The goal of this paper is to reconstruct finer-scale data from multiple coarse views, aggregated over different (subsets of) dimensions. The proposed method, called PREMA, leverages low-rank tensor factorization tools to provide recovery guarantees under certain conditions. PREMA is flexible in the sense that it can perform disaggregation on data that have missing entries, i.e., partially observed. The proposed method considers challenging scenarios: i) the available views of the data are aggregated in two dimensions, i.e., double aggregation, and ii) the aggregation patterns are unknown. Experiments on real data from different domains, i.e., sales data from retail companies, crime counts, and weather observations, are presented to showcase the effectiveness of PREMA.

A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. This paper presents an implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework achieves this by casting the DGP inference problem as a two-player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief. This consequently inspires us to devise a best-response dynamics algorithm to search for a Nash equilibrium (i.e., an unbiased posterior belief). Empirical evaluation shows that IPVI outperforms the state-of-the-art approximation methods for DGPs.

Expressiveness of deep models was recently addressed via the connection between neural networks (NNs) and kernel learning, where first-order dynamics of NN during a gradient-descent (GD) optimization were related to gradient similarity kernel, also known as Neural Tangent Kernel (NTK). In the majority of works this kernel is considered to be time-invariant, with its properties being defined entirely by NN architecture and independent of the learning task at hand. In contrast, in this paper we empirically explore these properties along the optimization and show that in practical applications the NN kernel changes in a very dramatic and meaningful way, with its top eigenfunctions aligning toward the target function learned by NN. Moreover, these top eigenfunctions serve sort of basis functions for NN output - a function represented by NN is spanned almost completely by them for the entire optimization process. Further, since the learning along top eigenfunctions is typically fast, their alignment with the target function improves the overall optimization performance. In addition, we study how the neural spectrum is affected by learning rate decay, typically done by practitioners, showing various trends in the kernel behavior. We argue that the presented phenomena may lead to a more complete theoretical understanding behind NN learning.

Question Can machine learning algorithms identify oncology patients at risk of short-term mortality to inform timely conversations between patients and physicians regrading serious illness? Findings In this cohort study of 26 525 patients seen in oncology practices within a large academic health system, machine learning algorithms accurately identified patients at high risk of 6-month mortality with good discrimination and positive predictive value. When the gradient boosting algorithm was applied in real time, most patients who were classified as having high risk were deemed appropriate by oncology clinicians for a conversation regarding serious illness. Meaning In this study, machine learning algorithms accurately identified patients with cancer who were at risk of 6-month mortality, suggesting that these models could facilitate more timely conversations between patients and physicians regarding goals and values. Importance Machine learning algorithms could identify patients with cancer who are at risk of short-term mortality. However, it is unclear how different machine learning algorithms compare and whether they could prompt clinicians to have timely conversations about treatment and end-of-life preferences. Objectives To develop, validate, and compare machine learning algorithms that use structured electronic health record data before a clinic visit to predict mortality among patients with cancer. Design, Setting, and Participants Cohort study of 26 525 adult patients who had outpatient oncology or hematology/oncology encounters at a large academic cancer center and 10 affiliated community practices between February 1, 2016, and July 1, 2016.