As people's demand for personal privacy and data security becomes a priority, encrypted traffic has become mainstream in the cyber world. However, traffic encryption is also shielding malicious and illegal traffic introduced by adversaries, from being detected. This is especially so in the post-COVID-19 environment where malicious traffic encryption is growing rapidly. Common security solutions that rely on plain payload content analysis such as deep packet inspection are rendered useless. Thus, machine learning based approaches have become an important direction for encrypted malicious traffic detection. In this paper, we formulate a universal framework of machine learning based encrypted malicious traffic detection techniques and provided a systematic review. Furthermore, current research adopts different datasets to train their models due to the lack of well-recognized datasets and feature sets. As a result, their model performance cannot be compared and analyzed reliably. Therefore, in this paper, we analyse, process and combine datasets from 5 different sources to generate a comprehensive and fair dataset to aid future research in this field. On this basis, we also implement and compare 10 encrypted malicious traffic detection algorithms. We then discuss challenges and propose future directions of research.

Despite their high predictive performance, random forest and gradient boosting are often considered as black boxes or uninterpretable models which has raised concerns from practitioners and regulators. As an alternative, we propose in this paper to use partial linear models that are inherently interpretable. Specifically, this article introduces GAM-lasso (GAMLA) and GAM-autometrics (GAMA), denoted as GAM(L)A in short. GAM(L)A combines parametric and non-parametric functions to accurately capture linearities and non-linearities prevailing between dependent and explanatory variables, and a variable selection procedure to control for overfitting issues. Estimation relies on a two-step procedure building upon the double residual method. We illustrate the predictive performance and interpretability of GAM(L)A on a regression and a classification problem. The results show that GAM(L)A outperforms parametric models augmented by quadratic, cubic and interaction effects. Moreover, the results also suggest that the performance of GAM(L)A is not significantly different from that of random forest and gradient boosting.

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods. Recently, the idea of end-to-end training of neural networks with ordering supervision via continuous relaxation of the sorting function has been presented by Grover et al. [1]. The idea of ordering supervision is that the ground truth order of some samples is known while their absolute values remain unsupervised. This is done by integrating a sorting algorithm in the neural architecture.

Pattern classification with compact representation is an important component in machine intelligence. In this work, an analytic bridge solution is proposed for compressive classification. The proposal has been based upon solving a penalized error formulation utilizing an approximated $\ell_p$-norm. The solution comes in a primal form for over-determined systems and in a dual form for under-determined systems. While the primal form is suitable for problems of low dimension with large data samples, the dual form is suitable for problems of high dimension but with a small number of data samples. The solution has also been extended for problems with multiple classification outputs. Numerical studies based on simulated and real-world data validated the effectiveness of the proposed solution.

Model-agnostic meta-learning (MAML) and its variants have become popular approaches for few-shot learning. However, due to the non-convexity of deep neural nets (DNNs) and the bi-level formulation of MAML, the theoretical properties of MAML with DNNs remain largely unknown. In this paper, we first prove that MAML with over-parameterized DNNs is guaranteed to converge to global optima at a linear rate. Our convergence analysis indicates that MAML with over-parameterized DNNs is equivalent to kernel regression with a novel class of kernels, which we name as Meta Neural Tangent Kernels (MetaNTK). Then, we propose MetaNTK-NAS, a new training-free neural architecture search (NAS) method for few-shot learning that uses MetaNTK to rank and select architectures. Empirically, we compare our MetaNTK-NAS with previous NAS methods on two popular few-shot learning benchmarks, miniImageNet, and tieredImageNet. We show that the performance of MetaNTK-NAS is comparable or better than the state-of-the-art NAS method designed for few-shot learning while enjoying more than 100x speedup. We believe the efficiency of MetaNTK-NAS makes itself more practical for many real-world tasks.

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in compressed sensing. From the perspective of statistical learning, another fundamental question is how well the IHT estimation would predict on unseen data. This paper makes progress towards answering this open question by introducing a novel sparse generalization theory for IHT under the notion of algorithmic stability. Our theory reveals that: 1) under natural conditions on the empirical risk function over $n$ samples of dimension $p$, IHT with sparsity level $k$ enjoys an $\mathcal{\tilde O}(n^{-1/2}\sqrt{k\log(n)\log(p)})$ rate of convergence in sparse excess risk; 2) a tighter $\mathcal{\tilde O}(n^{-1/2}\sqrt{\log(n)})$ bound can be established by imposing an additional iteration stability condition on a hypothetical IHT procedure invoked to the population risk; and 3) a fast rate of order $\mathcal{\tilde O}\left(n^{-1}k(\log^3(n)+\log(p))\right)$ can be derived for strongly convex risk function under proper strong-signal conditions. The results have been substantialized to sparse linear regression and sparse logistic regression models to demonstrate the applicability of our theory. Preliminary numerical evidence is provided to confirm our theoretical predictions.

Light-induced chemical processes are ubiquitous in nature and have widespread technological applications. For example, photoisomerization can allow a drug with a photo-switchable scaffold such as azobenzene to be activated with light. In principle, photoswitches with desired photophysical properties like high isomerization quantum yields can be identified through virtual screening with reactive simulations. In practice, these simulations are rarely used for screening, since they require hundreds of trajectories and expensive quantum chemical methods to account for non-adiabatic excited state effects. Here we introduce a diabatic artificial neural network (DANN) based on diabatic states to accelerate such simulations for azobenzene derivatives. The network is six orders of magnitude faster than the quantum chemistry method used for training. DANN is transferable to azobenzene molecules outside the training set, predicting quantum yields for unseen species that are correlated with experiment. We use the model to virtually screen 3,100 hypothetical molecules, and identify novel species with extremely high predicted quantum yields. The model predictions are confirmed using high accuracy non-adiabatic dynamics. Our results pave the way for fast and accurate virtual screening of photoactive compounds.

We introduce Consistent Assignment for Representation Learning (CARL), an unsupervised learning method to learn visual representations by combining ideas from self-supervised contrastive learning and deep clustering. By viewing contrastive learning from a clustering perspective, CARL learns unsupervised representations by learning a set of general prototypes that serve as energy anchors to enforce different views of a given image to be assigned to the same prototype. Unlike contemporary work on contrastive learning with deep clustering, CARL proposes to learn the set of general prototypes in an online fashion, using gradient descent without the necessity of using non-differentiable algorithms or K-Means to solve the cluster assignment problem. CARL surpasses its competitors in many representations learning benchmarks, including linear evaluation, semi-supervised learning, and transfer learning.

Recent development of advanced sensing and high computing technologies has enabled the wide adoption of machine vision to automatically inspect products' dimensional quality for efficient process control and reducing the manual inspection cost. The process control procedure requires effective data analysis methods to provide reliable inspection results. In this paper, we consider a high-volume manufacturing system that uses machine vision at the quality inspection station for automatic classification of product defects. Here classification implies both; identifying a defect and classifying its corresponding type. As a motivating example, we consider the scenario where batches of three-dimensional (3D) point cloud data are independently collected from a manufacturing process. The 3D point cloud data is obtained by measuring the 3D location of points on the product surface using a 3D scanner. The location measurements can then be used for fast classification of surface defects, and thus provide timely feedback for process control. Figure 1 (right) shows some exemplar surface defects on a wood product and the corresponding 3D point cloud measurements. The 3D point cloud measurements have a set of defining characteristics that should be considered in the development of defect classification techniques.

However, the development of a rigorous mathematical foundation is still at an early stage. In this survey article, which is based on an invited lecture at the International Congress of Mathematicians 2022, we will in particular focus on the current "workhorse" of artificial intelligence, namely deep neural networks. We will present the main theoretical directions along with several exemplary results and discuss key open problems.