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In this paper, we study kernel ridge-less regression, including the case of interpolating solutions. We prove that maximizing the leave-one-out ([Formula: see text]) stability minimizes the expected error. Further, we also prove that the minimum norm solution — to which gradient algorithms are known to converge — is the most stable solution. More precisely, we show that the minimum norm interpolating solution minimizes a bound on [Formula: see text] stability, which in turn is controlled by the smallest singular value, hence the condition number, of the empirical kernel matrix. These quantities can be characterized in the asymptotic regime where both the dimension ([Formula: see text]) and cardinality ([Formula: see text]) of the data go to infinity (with [Formula: see text] as [Formula: see text]). Our results suggest that the property of [Formula: see text] stability of the learning algorithm with respect to perturbations of the training set may provide a more general framework than the classical theory of Empirical Risk Minimization (ERM). While ERM was developed to deal with the classical regime in which the architecture of the learning network is fixed and [Formula: see text], the modern regime focuses on interpolating regressors and overparameterized models, when both [Formula: see text] and [Formula: see text] go to infinity. Since the stability framework is known to be equivalent to the classical theory in the classical regime, our results here suggest that it may be interesting to extend it beyond kernel regression to other overparameterized algorithms such as deep networks.

It has been empirically observed that the flatness of minima obtained from training deep networks seems to correlate with better generalization. However, for deep networks with positively homogeneous activations, most measures of flatness are not invariant to rescaling of the network parameters. This means that the measure of flatness can be made as small or as large as possible through rescaling, rendering the quantitative measures meaningless. In this paper we show that for deep networks with positively homogenous activations, these rescalings constitute equivalence relations, and that these equivalence relations induce a quotient manifold structure in the parameter space. Using an appropriate Riemannian metric, we propose a Hessian-based measure for flatness that is invariant to rescaling and perform simulations to empirically verify our claim. Finally we perform experiments to verify that our flatness measure correlates with generalization by using minibatch stochastic gradient descent with different batch sizes to find deep network minima with different generalization properties.

The pixel-wise code exposure (PCE) camera is a compressive sensing camera that has several advantages, such as low power consumption and high compression ratio. Moreover, one notable advantage is the capability to control individual pixel exposure time. Conventional approaches of using PCE cameras involve a time-consuming and lossy process to reconstruct the original frames and then use those frames for target tracking and classification. Otherwise, conventional approaches will fail if compressive measurements are used. In this paper, we present a deep learning approach that directly performs target tracking and classification in the compressive measurement domain without any frame reconstruction. Our approach has two parts: tracking and classification. The tracking has been done via detection using You Only Look Once (YOLO), and the classification is achieved using residual network (ResNet). Extensive simulations using short-wave infrared (SWIR) videos demonstrated the efficacy of our proposed approach.

Pixel-wise Code Exposure (PCE) camera is one type of compressive sensing camera that has low power consumption and high compression ratio. Moreover, a PCE camera can control individual pixel exposure time that can enable high dynamic range. Conventional approaches of using PCE camera involve a time consuming and lossy process to reconstruct the original frames and then use those frames for target tracking and classification. In this paper, we present a deep learning approach that directly performs target tracking and classification in the compressive measurement domain without any frame reconstruction. Our approach has two parts: tracking and classification. The tracking has been done using YOLO (You Only Look Once) and the classification is achieved using Residual Network (ResNet). Extensive experiments using mid-wave infrared (MWIR) and long-wave infrared (LWIR) videos demonstrated the efficacy of our proposed approach.

Modern ultra-wideband (UWB) radar systems transmit a wide range of frequencies, spanning hundreds of MHz to a few GHz, to achieve improved penetration depth and narrower pulse width. A common challenge faced is the presence of other commercial transmission equipment operating in the same band, causing radio frequency interference (RFI). To overcome this RFI issue, radar systems have been developed to either avoid operating in bands with RFI or suppress the RFI after reception. In this work, we examine both families of operation and demonstrate that 1D convolutional neural networks based on the UNet architecture can provide powerful signal enhancement capabilities on raw UWB radar data. The model is trained purely on simulated data and translated to real UWB data, achieving impressive results compared to traditional sparse-recovery baseline algorithms.

Discovering the underlying dynamics leading up to an industrial asset failure is an important problem to be solved for successful development of Predictive Maintenance techniques. Existing work has largely focused on building complex ML/AI models for developing Predictive Maintenance solution patterns, but has largely avoided developing methods to explain the underlying failure dynamics. In this paper, we use an old but significantly improved change-pattern based technique to analyze IoT sensor data and failure information to generate useful and interpretable failure-centric insight. We discuss a solution pattern that we call ChieF, which when applied on multi-variate time series datasets, discover the leading failure indicators, generate associative patterns among multiple features, and output temporal dynamics of changes. Experimental analysis of ChieF on four datasets uncovers insights that may be valuable for predictive maintenance.

One key advantage of compressive sensing is that only a small amount of the raw video data is transmitted or saved. This is extremely important in bandwidth constrained applications. Moreover, in some scenarios, the local processing device may not have enough processing power to handle object detection and classification and hence the heavy duty processing tasks need to be done at a remote location. Conventional compressive sensing schemes require the compressed data to be reconstructed first before any subsequent processing can begin. This is not only time consuming but also may lose important information in the process. In this paper, we present a real-time framework for processing compressive measurements directly without any image reconstruction. A special type of compressive measurement known as pixel-wise coded exposure (PCE) is adopted in our framework. PCE condenses multiple frames into a single frame. Individual pixels can also have different exposure times to allow high dynamic ranges. A deep learning tool known as You Only Look Once (YOLO) has been used in our real-time system for object detection and classification. Extensive experiments showed that the proposed real-time framework is feasible and can achieve decent detection and classification performance.

Conventional image discrimination tasks are performed on fully observed images. In challenging real imaging scenarios, where sensing systems are energy demanding or need to operate with limited bandwidth and exposure-time budgets, or defective pixels, where the data collected often suffers from missing information, and this makes the task extremely hard. In this paper, we leverage Convolutional Neural Networks (CNNs) to extract information from partially observed images. While pre-trained CNNs fail significantly even with such a small percentage of the input missing, our proposed framework demonstrates the ability to overcome it after training on fully-observed and partially-observed images at a few observation ratios. We demonstrate that our method is indeed reconstruction-free, retraining-free and generalizable to previously untrained-on observation ratios and it remains effective in two different visual tasks – image classification and object detection. Our framework performs well even for test images with only 10% of pixels available and outperforms the reconstruct-then-classify pipeline in these challenging scenarios for small observation fractions.

In this paper we study the unmixing problem which aims to separate a set of structured signals from their superposition. In this paper, we consider the scenario in which the mixture is observed via nonlinear compressive measurements. We present a fast, robust, greedy algorithm called Unmixing Matching Pursuit (UnmixMP) to solve this problem. We prove rigorously that the algorithm can recover the constituents from their noisy nonlinear compressive measurements with arbitrarily small error. We compare our algorithm to the Demixing with Hard Thresholding (DHT) algorithm [1], in a number of experiments on synthetic and real data.

In "Dictionary Learning" one tries to recover incoherent matrices $A^* \in \mathbb{R}^{n \times h}$ (typically overcomplete and whose columns are assumed to be normalized) and sparse vectors $x^* \in \mathbb{R}^h$ with a small support of size $h^p$ for some $0, Comment: In this new version of the paper with a small change in the distributional assumptions we are actually able to prove the asymptotic criticality of a neighbourhood of the ground truth dictionary for even just the standard squared loss of the ReLU autoencoder (unlike the regularized loss in the older version)

We present a Recurrent Neural Network using LSTM (Long Short Term Memory) that is capable of modeling and predicting Local Field Potentials. We train and test the network on real data recorded from epilepsy patients. We construct networks that predict multi-channel LFPs for 1, 10, and 100 milliseconds forward in time. Our results show that prediction using LSTM outperforms regression when predicting 10 and 100 millisecond forward in time.

Compressive sensing has seen many applications in recent years. One type of compressive sensing device is the Pixel-wise Code Exposure (PCE) camera, which has low power consumption and individual control of pixel exposure time. In order to use PCE cameras for practical applications, a time consuming and lossy process is needed to reconstruct the original frames. In this paper, we present a deep learning approach that directly performs target tracking and classification in the compressive measurement domain without any frame reconstruction. In particular, we propose to apply You Only Look Once (YOLO) to detect and track targets in the frames and we propose to apply Residual Network (ResNet) for classification. Extensive simulations using low quality optical and mid-wave infrared (MWIR) videos in the SENSIAC database demonstrated the efficacy of our proposed approach.

In this paper, we develop Targeted Dot Product Representation (TarDPR), a DPR-based feature selection and combination framework for friend recommendation in online social networks (OSNs). Our approach modifies conventional DPR techniques and makes itself applicable to OSNs by focusing on computing a consistent representation while minimizing unnecessary suggestions made outside these interested regions. A notable property of TarDPR is its ability to effectively incorporate different types of social features and produce new meaningful features that help competitive approaches to significantly improve their recommendation quality. We derive an iterative algorithm for TarDPR that is supported by mathematical analysis, and is efficient on large social traces. To certify the usability of our approach, we conduct empirical experiments on real social traces including Facebook and Foursquare social networks. The competitive experimental results show that TarDPR achieves up to 15% improvement in comparison with other competitive methods. These results consequently confirm the efficacy of our suggested framework.