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In this paper, we prove a compressive sensing guarantee for restricted measurement domains in spherical near-field to far-field transformations for antenna metrology. We do so by first defining Slepian functions on a measurement sub-domain $R$ of the rotation group $\mathrm{SO}(3)$, the full domain of the linear inverse problem associated with spherical near-field to far-field transformations. Then, we transform the inverse problem from the measurement basis, the bounded orthonormal system of band-limited Wigner $D$-functions on $\mathrm{SO}(3)$, to the Slepian functions in a way that preserves sparsity. Contrasting methods using Wigner $D$-functions that require measurements on all of $\mathrm{SO}(3)$, we show that the orthogonality structure of the Slepian functions only requires measurements on the sub-domain $R$, which is select-able. Due to the particulars of this approach and the inherent presence of Slepian functions with low concentrations on $R$, our approach gives the highest accuracy when the signal under study is well concentrated on $R$. We provide numerical examples of our method in comparison with other classical and compressive sensing approaches. In terms of reconstruction quality, we find that our method outperforms the other compressive sensing approaches we test and is at least as good as classical approaches but with a significant reduction in the number of measurements.

Heart Disease has become one of the most serious diseases that has a significant impact on human life. It has emerged as one of the leading causes of mortality among the people across the globe during the last decade. In order to prevent patients from further damage, an accurate diagnosis of heart disease on time is an essential factor. Recently we have seen the usage of non-invasive medical procedures, such as artificial intelligence-based techniques in the field of medical. Specially machine learning employs several algorithms and techniques that are widely used and are highly useful in accurately diagnosing the heart disease with less amount of time. However, the prediction of heart disease is not an easy task. The increasing size of medical datasets has made it a complicated task for practitioners to understand the complex feature relations and make disease predictions. Accordingly, the aim of this research is to identify the most important risk-factors from a highly dimensional dataset which helps in the accurate classification of heart disease with less complications. For a broader analysis, we have used two heart disease datasets with various medical features. The classification results of the benchmarked models proved that there is a high impact of relevant features on the classification accuracy. Even with a reduced number of features, the performance of the classification models improved significantly with a reduced training time as compared with models trained on full feature set.

The analysis and optimization of single intelligent reflecting surface (IRS)-assisted systems have been extensively studied, whereas little is known regarding multiple-IRS-assisted systems. This paper investigates the analysis and optimization of a double-IRS cooperatively assisted downlink system, where a multi-antenna base station (BS) serves a single-antenna user with the help of two multi-element IRSs, connected by an inter-IRS channel. The channel between any two nodes is modeled with Rician fading. The BS adopts the instantaneous CSI-adaptive maximum-ratio transmission (MRT) beamformer, and the two IRSs adopt a cooperative quasi-static phase shift design. The goal is to maximize the average achievable rate, which can be reflected by the average channel power of the equivalent channel between the BS and user, at a low phase adjustment cost and computational complexity. First, we obtain tractable expressions of the average channel power of the equivalent channel in the general Rician factor, pure line of sight (LoS), and pure non-line of sight (NLoS) regimes, respectively. Then, we jointly optimize the phase shifts of the two IRSs to maximize the average channel power of the equivalent channel in these regimes. The optimization problems are challenging non-convex problems. We obtain globally optimal closed-form solutions for some cases and propose computationally efficient iterative algorithms to obtain stationary points for the other cases. Next, we compare the computational complexity for optimizing the phase shifts and the optimal average channel power of the double-IRS cooperatively assisted system with those of a counterpart single-IRS-assisted system at a large number of reflecting elements in the three regimes. Finally, we numerically demonstrate notable gains of the proposed solutions over the existing solutions at different system parameters.

In this paper, we propose a weak approximation of the reflection coupling (RC) for stochastic differential equations (SDEs), and prove it converges weakly to the desired coupling. In contrast to the RC, the proposed approximate reflection coupling (ARC) need not take the hitting time of processes to the diagonal set into consideration and can be defined as the solution of some SDEs on the whole time interval. Therefore, ARC can work effectively against SDEs with different drift terms. As an application of ARC, an evaluation on the effectiveness of the stochastic gradient descent in a non-convex setting is also described. For the sample size $n$, the step size $\eta$, and the batch size $B$, we derive uniform evaluations on the time with orders $n^{-1}$, $\eta^{1/2}$, and $\sqrt{(n - B) / B (n - 1)}$, respectively.

EMG (Electromyograph) signal based gesture recognition can prove vital for applications such as smart wearables and bio-medical neuro-prosthetic control. Spiking Neural Networks (SNNs) are promising for low-power, real-time EMG gesture recognition, owing to their inherent spike/event driven spatio-temporal dynamics. In literature, there are limited demonstrations of neuromorphic hardware implementation (at full chip/board/system scale) for EMG gesture classification. Moreover, most literature attempts exploit primitive SNNs based on LIF (Leaky Integrate and Fire) neurons. In this work, we address the aforementioned gaps with following key contributions: (1) Low-power, high accuracy demonstration of EMG-signal based gesture recognition using neuromorphic Recurrent Spiking Neural Networks (RSNN). In particular, we propose a multi-time scale recurrent neuromorphic system based on special double-exponential adaptive threshold (DEXAT) neurons. Our network achieves state-of-the-art classification accuracy (90%) while using ~53% lesser neurons than best reported prior art on Roshambo EMG dataset. (2) A new multi-channel spike encoder scheme for efficient processing of real-valued EMG data on neuromorphic systems. (3) Unique multi-compartment methodology to implement complex adaptive neurons on Intel's dedicated neuromorphic Loihi chip is shown. (4) RSNN implementation on Loihi (Nahuku 32) achieves significant energy/latency benefits of ~983X/19X compared to GPU for batch size as 50.

Rate splitting (RS) systems can better deal with imperfect channel state information at the transmitter (CSIT) than conventional approaches. However, this requires an appropriate power allocation that often has a high computational complexity, which might be inadequate for practical and large systems. To this end, adaptive power allocation techniques can provide good performance with low computational cost. This work presents novel robust and adaptive power allocation technique for RS-based multiuser multiple-input multiple-output (MU-MIMO) systems. In particular, we develop a robust adaptive power allocation based on stochastic gradient learning and the minimization of the mean-square error between the transmitted symbols of the RS system and the received signal. The proposed robust power allocation strategy incorporates knowledge of the variance of the channel errors to deal with imperfect CSIT and adjust power levels in the presence of uncertainty. An analysis of the convexity and stability of the proposed power allocation algorithms is provided, together with a study of their computational complexity and theoretical bounds relating the power allocation strategies. Numerical results show that the sum-rate of an RS system with adaptive power allocation outperforms RS and conventional MU-MIMO systems under imperfect CSIT. %\vspace{-0.75em}

Bayesian networks have been used as a mechanism to represent the joint distribution of multiple random variables in a flexible yet interpretable manner. One major challenge in learning the structure of a network is how to model networks which include a mixture of continuous and discrete random variables, known as hybrid Bayesian networks. This paper reviews the literature on approaches to handle hybrid Bayesian networks. When working with hybrid Bayesian networks, typically one of two approaches is taken: either the data are considered to have a joint multivariate Gaussian distribution, irrespective of the true distribution, or continuous random variables are discretized, resulting in discrete Bayesian networks. In this paper, we show that a strategy to model all random variables as Gaussian outperforms the strategy which converts the continuous random variables to discrete. We demonstrate the superior performance of our strategy over the latter, theoretically and by simulation studies for various settings. Both strategies are also implemented on a childhood obesity data set. The two different strategies give rise to significant differences in the optimal graph structures, with the results of the simulation study suggesting that the inference from the strategy assuming all random variables are Gaussian is more reliable.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.

Current deep learning research is dominated by benchmark evaluation. A method is regarded as favorable if it empirically performs well on the dedicated test set. This mentality is seamlessly reflected in the resurfacing area of continual learning, where consecutively arriving sets of benchmark data are investigated. The core challenge is framed as protecting previously acquired representations from being catastrophically forgotten due to the iterative parameter updates. However, comparison of individual methods is nevertheless treated in isolation from real world application and typically judged by monitoring accumulated test set performance. The closed world assumption remains predominant. It is assumed that during deployment a model is guaranteed to encounter data that stems from the same distribution as used for training. This poses a massive challenge as neural networks are well known to provide overconfident false predictions on unknown instances and break down in the face of corrupted data. In this work we argue that notable lessons from open set recognition, the identification of statistically deviating data outside of the observed dataset, and the adjacent field of active learning, where data is incrementally queried such that the expected performance gain is maximized, are frequently overlooked in the deep learning era. Based on these forgotten lessons, we propose a consolidated view to bridge continual learning, active learning and open set recognition in deep neural networks. Our results show that this not only benefits each individual paradigm, but highlights the natural synergies in a common framework. We empirically demonstrate improvements when alleviating catastrophic forgetting, querying data in active learning, selecting task orders, while exhibiting robust open world application where previously proposed methods fail.