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Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that wide ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special architectural re-design. 

The frequency-dependent nature of hearing loss poses many challenges for hearing aid design. In order to compensate for a hearing aid user’s unique hearing loss pattern, an input signal often needs to be separated into frequency bands, or channels, through a process called sub-band decomposition. In this paper, we present a real-time filter bank for hearing aids. Our filter bank features 10 channels uniformly distributed on the logarithmic scale, located at the standard audiometric frequencies used for the characterization and fitting of hearing aids. We obtained filters with very narrow passbands in the lower frequencies by employing multi-rate signal processing. Our filter bank offers a 9.1× reduction in complexity as compared to conventional signal processing. We implemented our filter bank on Open Speech Platform, an open-source hearing aid, and confirmed real-time operation. 

We propose a new adaptive feedback cancellation (AFC) system in hearing aids (HAs) based on a well-posed optimization criterion that jointly considers both decorrelation of the signals and sparsity of the underlying channel. We show that the least squares criterion on subband errors regularized by a p-norm-like diversity measure can be used to simultaneously decorrelate the speech signals and exploit sparsity of the acoustic feedback path impulse response. Compared with traditional subband adaptive filters that are not appropriate for incorporating sparsity due to shorter sub-filters, our proposed framework is suitable for promoting sparse characteristics, as the update rule utilizing subband information actually operates in the fullband. Simulation results show that the normalized misalignment, added stable gain, and other objective metrics of the AFC are significantly improved by choosing a proper sparsity promoting factor and a suitable number of subbands. More importantly, the results indicate that the benefits of subband decomposition and sparsity promoting are complementary and additive for AFC in HAs. 

While deep neural networks (DNNs) have achieved state-of-the-art results in many fields, they are typically over-parameterized. Parameter redundancy, in turn, leads to inefficiency. Sparse signal recovery (SSR) techniques, on the other hand, find compact solutions to over-complete linear problems. Therefore, a logical step is to draw the connection between SSR and DNNs. In this paper, we explore the application of iterative reweighting methods popular in SSR to learning efficient DNNs. By efficient, we mean sparse networks that require less computation and storage than the original, dense network. We propose a reweighting framework to learn sparse connections within a given architecture without biasing the optimization process, by utilizing the affine scaling transformation strategy. The resulting algorithm, referred to as Sparsity-promoting Stochastic Gradient Descent (SSGD), has simple gradient-based updates which can be easily implemented in existing deep learning libraries. We demonstrate the sparsification ability of SSGD on image classification tasks and show that it outperforms existing methods on the MNIST and CIFAR-10 datasets. 

We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion directly penalizes subband errors and includes a sparsity penalty term which is minimized using the damped regularized Newton’s method. The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the system identification problem via computer simulations. Specifically, we study the effects of using different numbers of subbands and various sparsity penalty terms for quasi-sparse, sparse, and dispersive systems. The results show that the benefit of increasing the number of subbands is larger than promoting sparsity of the estimated filter coefficients when the target system is quasi-sparse or dispersive. On the other hand, for sparse target systems, promoting sparsity becomes more important. More importantly, the two aspects provide complementary and additive benefits to the GPtNSAF for speeding up convergence. 

In this paper, a novel way of deriving proportionate adaptive filters is proposed based on diversity measure minimization using the iterative reweighting techniques well-known in the sparse signal recovery (SSR) area. The resulting least mean square (LMS)-type and normalized LMS (NLMS)-type sparse adaptive filtering algorithms can incorporate various diversity measures that have proved effective in SSR. Furthermore, by setting the regularization coefficient of the diversity measure term to zero in the resulting algorithms, Sparsity promoting LMS (SLMS) and Sparsity promoting NLMS (SNLMS) are introduced, which exploit but do not strictly enforce the sparsity of the system response if it already exists. Moreover, unlike most existing proportionate algorithms that design the step-size control factors based on heuristics, our SSR-based framework leads to designing the factors in a more systematic way. Simulation results are presented to demonstrate the convergence behavior of the derived algorithms for systems with different sparsity levels.