There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Convex Analysisの二,三の進展について

On robust estimation of the location parameter

Nociceptor inputs can trigger a prolonged but reversible increase in the excitability and synaptic efficacy of neurons in central nociceptive pathways, the phenomenon of central sensitization. Central sensitization manifests as pain hypersensitivity, particularly dynamic tactile allodynia, secondary punctate or pressure hyperalgesia, aftersensations, and enhanced temporal summation. It can be readily and rapidly elicited in human volunteers by diverse experimental noxious conditioning stimuli to skin, muscles or viscera, and in addition to producing pain hypersensitivity, results in secondary changes in brain activity that can be detected by electrophysiological or imaging techniques. Studies in clinical cohorts reveal changes in pain sensitivity that have been interpreted as revealing an important contribution of central sensitization to the pain phenotype in patients with fibromyalgia, osteoarthritis, musculoskeletal disorders with generalized pain hypersensitivity, headache, temporomandibular joint disorders, dental pain, neuropathic pain, visceral pain hypersensitivity disorders and post-surgical pain. The comorbidity of those pain hypersensitivity syndromes that present in the absence of inflammation or a neural lesion, their similar pattern of clinical presentation and response to centrally acting analgesics, may reflect a commonality of central sensitization to their pathophysiology. An important question that still needs to be determined is whether there are individuals with a higher inherited propensity for developing central sensitization than others, and if so, whether this conveys an increased risk in both developing conditions with pain hypersensitivity, and their chronification. Diagnostic criteria to establish the presence of central sensitization in patients will greatly assist the phenotyping of patients for choosing treatments that produce analgesia by normalizing hyperexcitable central neural activity. We have certainly come a long way since the first discovery of activity-dependent synaptic plasticity in the spinal cord and the revelation that it occurs and produces pain hypersensitivity in patients. Nevertheless, discovering the genetic and environmental contributors to and objective biomarkers of central sensitization will be highly beneficial, as will additional treatment options to prevent or reduce this prevalent and promiscuous form of pain plasticity.

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Central sensitization: implications for the diagnosis and treatment of pain.

We analyze different direction based signal copy algorithms for a model of angular spread caused by local scattering around each signal source. Optimal algorithms, in terms of signal to interference and noise ratio, are derived for both rapidly and slowly time varying angular spread and a low complexity an-hoc algorithm is suggested. Simulations show that these algorithms outperform traditional signal copy algorithms in terms of signal to interference and noise ratio as well as outage probability.

Signal waveform estimation from array data in angular spread environment

The weighted minimum mean square error (WMMSE) algorithm was proposed to provide a locally optimum solution to the otherwise NP-hard weighted sum rate maximization beamforming problem, but it can still be prohibitively complex for real-time implementation. With the success of deep unfolding in trading off complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm. With respect to traditional end-to-end learning, deep unfolding incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the classical formulation of the WMMSE algorithm given by Shi et al. is not amenable for deep unfolding due to matrix inversions, eigendecompositions, and bisection searches. Therefore, we present an alternative formulation that circumvents these operations. By means of simulations, we show that the deep unfolded WMMSE algorithm performs on par with the original WMMSE algorithm, at a lower computational load.

Deep Weighted MMSE Downlink Beamforming

We consider scenarios such as IoT-based 5G or IoT-based machine type communication, where a low-cost low-power transmitter communicates with a high-quality receiver. Then, digital predistortion of the nonlinear power amplifier may be too expensive. In order to investigate the feasibility of receiver-side compensation of the transmitter RF impairments, we study joint maximum-likelihood estimation of channel and clipping level in multipath fading OFDM systems. In particular, we propose an alternative optimization algorithm, which uses frequency-domain block-type training symbols, and prove that this algorithm always converges, at least to a local optimum point. Then, we calculate the Cramer-Rao lower bound, and show that the proposed estimator attains it for high signal-to-noise ratios. Finally, we perform numerical evaluations to illustrate the performance of the estimator, and show that iterative decoding can be done using the estimated channel and clipping level with almost the same performance as a genie-aided scenario, where the channel and clipping level are perfectly known.

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Joint Channel and Clipping Level Estimation for OFDM in IoT-based Networks

CoMP transmission and reception have been considered in cellular networks for enabling larger coverage, improved rates, and interference mitigation. To harness the gains of coordinated beamforming, fast information exchange over a backhaul connecting the cooperating BSs is required. In practice, the bandwidth and delay limitations of the backhaul may not be able to meet such stringent demands. These impairments motivate the study of cooperative approaches based only on local CSI that require minimal or no information exchange between the BSs. To this end, several distributed approaches are introduced for CB-CoMP. The proposed methods rely on the channel reciprocity and iterative spatially precoded over-the-air pilot signaling. We elaborate how F-B training facilitates distributed CB by allowing BSs and UEs to iteratively optimize their respective transmitters/receivers based on only locally measured CSI. The trade-off due to the overhead from the F-B iterations is discussed. We also consider the challenge of dynamic TDD where the UE-UE channel knowledge cannot be acquired at the BSs by exploiting channel reciprocity. Finally, standardization activities and practical requirements for enabling the proposed F-B training schemes in 5G radio access are discussed.

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Distributed Coordinated Transmission with Forward-Backward Training for 5G Radio Access

In the context of wireless communications, we propose a deep learning approach to learn the mapping from the instantaneous state of a frequency selective fading channel to the corresponding frame error probability (FEP) for an arbitrary set of transmission parameters. We propose an abstract model of a bit interleaved coded modulation (BICM) orthogonal frequency division multiplexing (OFDM) link chain and show that the maximum likelihood (ML) estimator of the model parameters estimates the true FEP distribution. Further, we exploit deep neural networks as a general purpose tool to implement our model and propose a training scheme for which, even while training with the binary frame error events (i.e., ACKs / NACKs), the network outputs converge to the FEP conditioned on the input channel state. We provide simulation results that demonstrate gains in the FEP prediction accuracy with our approach as compared to the traditional effective exponential SIR metric (EESM) approach for a range of channel code rates, and show that these gains can be exploited to increase the link throughput.

Mats Bengtsson

Papers

Signal waveform estimation from array data in angular spread environment

Deep Weighted MMSE Downlink Beamforming

Joint Channel and Clipping Level Estimation for OFDM in IoT-based Networks

Distributed Coordinated Transmission with Forward-Backward Training for 5G Radio Access

Deep Learning for Frame Error Probability Prediction in BICM-OFDM Systems