We investigate time-dependent data analysis from the perspective of recurrent kernel machines, from which models with hidden units and gated memory cells arise naturally. By considering dynamic gating of the memory cell, a model closely related to the long short-term memory (LSTM) recurrent neural network is derived. Extending this setup to $n$-gram filters, the convolutional neural network (CNN), Gated CNN, and recurrent additive network (RAN) are also recovered as special cases. Our analysis provides a new perspective on the LSTM, while also extending it to $n$-gram convolutional filters. Experiments are performed on natural language processing tasks and on analysis of local field potentials (neuroscience). We demonstrate that the variants we derive from kernels perform on par or even better than traditional neural methods. For the neuroscience application, the new models demonstrate significant improvements relative to the prior state of the art.

Section 3 & 4 feels mostly independent of kernels, it reads as a train-of-thought discussion on how to motivate and build useful RNN architectures. It fails as a clear description of the actual proposed models, as it takes quite a bit of re-reading to detail and understand what the RKM-LSTM is, for example. For the language modelling experiments, I feel Table 3 should probably acknowledge what is state-of-the-art for WikiText-2 and PTB, as there's an insinuation that the proposed models are SOTA (which they are not). For example, [24] is cited however the numbers in their paper are actually better than what is presented in Table 3. E.g. for [24] PTB is 60.0 valid, 57.3 test; WT2 is 68.6 valid, 65.8 test. But there are more recent variants of the awd-lstm, e.g.

We investigate time-dependent data analysis from the perspective of recurrent kernel machines, from which models with hidden units and gated memory cells arise naturally. By considering dynamic gating of the memory cell, a model closely related to the long short-term memory (LSTM) recurrent neural network is derived. Extending this setup to n -gram filters, the convolutional neural network (CNN), Gated CNN, and recurrent additive network (RAN) are also recovered as special cases. Our analysis provides a new perspective on the LSTM, while also extending it to n -gram convolutional filters. Experiments are performed on natural language processing tasks and on analysis of local field potentials (neuroscience).

The objective of this Philosophiae Doctor (Ph.D) thesis is to propose an efficient approach for optimizing a multidisciplinary black-box model when the optimization problem is constrained and involves a large number of mixed integer design variables (typically 100 variables). The targeted optimization approach, called EGO, is based on a sequential enrichment of an adaptive surrogate model and, in this context, GP surrogate models are one of the most widely used in engineering problems to approximate time-consuming high fidelity models. EGO is a heuristic BO method that performs well in terms of solution quality. However, like any other global optimization method, EGO suffers from the curse of dimensionality, meaning that its performance is satisfactory on lower dimensional problems, but deteriorates as the dimensionality of the optimization search space increases. For realistic aircraft design problems, the typical size of the design variables can even exceed 100 and, thus, trying to solve directly the problems using EGO is ruled out. The latter is especially true when the problems involve both continuous and categorical variables increasing even more the size of the search space. In this Ph.D thesis, effective parameterization tools are investigated, including techniques like partial least squares regression, to significantly reduce the number of design variables. Additionally, Bayesian optimization is adapted to handle discrete variables and high-dimensional spaces in order to reduce the number of evaluations when optimizing innovative aircraft concepts such as the "DRAGON" hybrid airplane to reduce their climate impact.

Utilizing unmanned aerial vehicles (UAVs) with edge server to assist terrestrial mobile edge computing (MEC) has attracted tremendous attention. Nevertheless, state-of-the-art schemes based on deterministic optimizations or single-objective reinforcement learning (RL) cannot reduce the backlog of task bits and simultaneously improve energy efficiency in highly dynamic network environments, where the design problem amounts to a sequential decision-making problem. In order to address the aforementioned problems, as well as the curses of dimensionality introduced by the growing number of terrestrial terrestrial users, this paper proposes a distributed multi-objective (MO) dynamic trajectory planning and offloading scheduling scheme, integrated with MORL and the kernel method. The design of n-step return is also applied to average fluctuations in the backlog. Numerical results reveal that the n-step return can benefit the proposed kernel-based approach, achieving significant improvement in the long-term average backlog performance, compared to the conventional 1-step return design. Due to such design and the kernel-based neural network, to which decision-making features can be continuously added, the kernel-based approach can outperform the approach based on fully-connected deep neural network, yielding improvement in energy consumption and the backlog performance, as well as a significant reduction in decision-making and online learning time.

We investigate time-dependent data analysis from the perspective of recurrent kernel machines, from which models with hidden units and gated memory cells arise naturally. By considering dynamic gating of the memory cell, a model closely related to the long short-term memory (LSTM) recurrent neural network is derived. Extending this setup to $n$-gram filters, the convolutional neural network (CNN), Gated CNN, and recurrent additive network (RAN) are also recovered as special cases. Our analysis provides a new perspective on the LSTM, while also extending it to $n$-gram convolutional filters. Experiments are performed on natural language processing tasks and on analysis of local field potentials (neuroscience).

Causal learning is a beneficial approach to analyze the cause and effect relationships among variables in a dataset. A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast Causal Inference (FCI). Generating a causal graph from a dataset that contains different data types (mixed data) is not trivial. This research offers an easy way to handle the mixed data so that it can be used to learn causal graphs using the existing application of the PC algorithm and FCI. This research proposes using kernel functions and Kernel Alignment to handle a mixed data. Two main steps of this approach are computing a kernel matrix for each variable and calculating a pseudo-correlation matrix using Kernel Alignment. Kernel Alignment is used as a substitute for the correlation matrix for the conditional independence test for Gaussian data in PC Algorithm and FCI. The advantage of this idea is that is possible to handle any data type by using a suitable kernel function to compute a kernel matrix for an observed variable. The proposed method is successfully applied to learn a causal graph from a mixed data containing categorical, binary, ordinal, and continuous variables.

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$ coefficients of the nonlinearity together with the first $n$ samples of the impulse response of the linear system by estimating an $np$-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and $p$ coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.

In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.