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In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference approximations of the derivatives. We use a special adaptive search procedure in our algorithms, which simultaneously fits both the regularization constant and the parameters of the finite difference approximations. It makes our schemes free from the need to know the actual Lipschitz constants. Additionally, we equip our algorithms with the lazy Hessian update that reuse a previously computed Hessian approximation matrix for several iterations. Specifically, we prove the global complexity bound of $\mathcal{O}( n^{1/2} \epsilon^{-3/2})$ function and gradient evaluations for our new Hessian-free method, and a bound of $\mathcal{O}( n^{3/2} \epsilon^{-3/2} )$ function evaluations for the derivative-free method, where $n$ is the dimension of the problem and $\epsilon$ is the desired accuracy for the gradient norm. These complexity bounds significantly improve the previously known ones in terms of the joint dependence on $n$ and $\epsilon$, for the first-order and zeroth-order non-convex optimization.

Music Structure Analysis (MSA) is the task aiming at identifying musical segments that compose a music track and possibly label them based on their similarity. In this paper we propose a supervised approach for the task of music boundary detection. In our approach we simultaneously learn features and convolution kernels. For this we jointly optimize -- a loss based on the Self-Similarity-Matrix (SSM) obtained with the learned features, denoted by SSM-loss, and -- a loss based on the novelty score obtained applying the learned kernels to the estimated SSM, denoted by novelty-loss. We also demonstrate that relative feature learning, through self-attention, is beneficial for the task of MSA. Finally, we compare the performances of our approach to previously proposed approaches on the standard RWC-Pop, and various subsets of SALAMI.

The task of natural language inference (NLI) asks whether a given premise (expressed in NL) entails a given NL hypothesis. NLI benchmarks contain human ratings of entailment, but the meaning relationships driving these ratings are not formalized. Can the underlying sentence pair relationships be made more explicit in an interpretable yet robust fashion? We compare semantic structures to represent premise and hypothesis, including sets of contextualized embeddings and semantic graphs (Abstract Meaning Representations), and measure whether the hypothesis is a semantic substructure of the premise, utilizing interpretable metrics. Our evaluation on three English benchmarks finds value in both contextualized embeddings and semantic graphs; moreover, they provide complementary signals, and can be leveraged together in a hybrid model.

We propose a novel algorithm for solving the composite Federated Learning (FL) problem. This algorithm manages non-smooth regularization by strategically decoupling the proximal operator and communication, and addresses client drift without any assumptions about data similarity. Moreover, each worker uses local updates to reduce the communication frequency with the server and transmits only a $d$-dimensional vector per communication round. We prove that our algorithm converges linearly to a neighborhood of the optimal solution and demonstrate the superiority of our algorithm over state-of-the-art methods in numerical experiments.

The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower decay in the variance of the MLMC correction. This article reviews the literature on techniques which can be used to overcome this challenge in a variety of different contexts, and discusses recent developments using either a branching diffusion or adaptive sampling.

Recently, a stability theory has been developed to study the linear stability of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the convergence of an MPRK scheme towards the steady state of the corresponding initial value problem, whereas the main assumption is that the initial value is sufficiently close to the steady state. Initially, numerical experiments in several publications indicated that these linear stability properties are not only local, but even global, as is the case for general linear methods. Recently, however, it was discovered that the linear stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture is that this is a result of negative Runge--Kutta (RK) parameters of MPDeC(8) and that linear stability is indeed global, if the RK parameters are nonnegative. To support this conjecture, we examine the family of MPRK22($\alpha$) methods with negative RK parameters and show that even among these methods there are methods for which the stability properties are only local. However, this local linear stability is not observed for MPRK22($\alpha$) schemes with nonnegative Runge-Kutta parameters.

Trojans are one of the most threatening network attacks currently. HTTP-based Trojan, in particular, accounts for a considerable proportion of them. Moreover, as the network environment becomes more complex, HTTP-based Trojan is more concealed than others. At present, many intrusion detection systems (IDSs) are increasingly difficult to effectively detect such Trojan traffic due to the inherent shortcomings of the methods used and the backwardness of training data. Classical anomaly detection and traditional machine learning-based (TML-based) anomaly detection are highly dependent on expert knowledge to extract features artificially, which is difficult to implement in HTTP-based Trojan traffic detection. Deep learning-based (DL-based) anomaly detection has been locally applied to IDSs, but it cannot be transplanted to HTTP-based Trojan traffic detection directly. To solve this problem, in this paper, we propose a neural network detection model (HSTF-Model) based on hierarchical spatiotemporal features of traffic. Meanwhile, we combine deep learning algorithms with expert knowledge through feature encoders and statistical characteristics to improve the self-learning ability of the model. Experiments indicate that F1 of HSTF-Model can reach 99.4% in real traffic. In addition, we present a dataset BTHT consisting of HTTP-based benign and Trojan traffic to facilitate related research in the field.

Building on Dryden et al. (2021), this note presents the Bayesian estimation of a regression model for size-and-shape response variables with Gaussian landmarks. Our proposal fits into the framework of Bayesian latent variable models and allows a highly flexible modelling framework.

In Generalized Linear Models (GLMs) it is assumed that there is a linear effect of the predictor variables on the outcome. However, this assumption is often too strict, because in many applications predictors have a nonlinear relation with the outcome. Optimal Scaling (OS) transformations combined with GLMs can deal with this type of relations. Transformations of the predictors have been integrated in GLMs before, e.g. in Generalized Additive Models. However, the OS methodology has several benefits. For example, the levels of categorical predictors are quantified directly, such that they can be included in the model without defining dummy variables. This approach enhances the interpretation and visualization of the effect of different levels on the outcome. Furthermore, monotonicity restrictions can be applied to the OS transformations such that the original ordering of the category values is preserved. This improves the interpretation of the effect and may prevent overfitting. The scaling level can be chosen for each individual predictor such that models can include mixed scaling levels. In this way, a suitable transformation can be found for each predictor in the model. The implementation of OS in logistic regression is demonstrated using three datasets that contain a binary outcome variable and a set of categorical and/or continuous predictor variables.