Typical R-convolution graph kernels invoke the kernel functions that decompose graphs into non-isomorphic substructures and compare them. However, overlooking implicit similarities and topological position information between those substructures limits their performances. In this paper, we introduce Deep Hierarchical Graph Alignment Kernels (DHGAK) to resolve this problem. Specifically, the relational substructures are hierarchically aligned to cluster distributions in their deep embedding space. The substructures belonging to the same cluster are assigned the same feature map in the Reproducing Kernel Hilbert Space (RKHS), where graph feature maps are derived by kernel mean embedding. Theoretical analysis guarantees that DHGAK is positive semi-definite and has linear separability in the RKHS. Comparison with state-of-the-art graph kernels on various benchmark datasets demonstrates the effectiveness and efficiency of DHGAK. The code is available at Github (https://github.com/EWesternRa/DHGAK).

Softmax distributions are widely used in machine learning, including Large Language Models (LLMs) where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the model produces an output drawn from the softmax distribution (which depends on the vector input). We consider the fundamental problem of binary hypothesis testing in the setting of softmax models. That is, given an unknown softmax model, which is known to be one of the two given softmax models, how many queries are needed to determine which one is the truth? We show that the sample complexity is asymptotically $O(\epsilon^{-2})$ where $\epsilon$ is a certain distance between the parameters of the models. Furthermore, we draw analogy between the softmax model and the leverage score model, an important tool for algorithm design in linear algebra and graph theory. The leverage score model, on a high level, is a model which, given vector input, produces an output drawn from a distribution dependent on the input. We obtain similar results for the binary hypothesis testing problem for leverage score models.

The Twelfth International Conference on Learning Representations (ICLR) is taking place this week in Vienna, Austria. During the opening of the conference, the outstanding paper award winners, and honourable mentions, were announced. The conference organisers also introduced a new award for this year: the test of time award. This award honours a paper from 2013/2014 that the programme chairs judge to have had a lasting impact. Abstract: How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets?

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art Markov chain Monte Carlo technique, exploiting the shape of such high-dimensional target distributions to efficiently generate samples. Despite its impressive empirical success and increasing popularity, its wide-scale adoption remains limited due to the high computational cost of gradient calculation. Moreover, applying this method is impossible when the gradient of the posterior cannot be computed (for example, with black-box simulators). To overcome these challenges, we propose a novel two-stage Hamiltonian Monte Carlo algorithm with a surrogate model. In this multi-fidelity algorithm, the acceptance probability is computed in the first stage via a standard HMC proposal using an inexpensive differentiable surrogate model, and if the proposal is accepted, the posterior is evaluated in the second stage using the high-fidelity (HF) numerical solver. Splitting the standard HMC algorithm into these two stages allows for approximating the gradient of the posterior efficiently, while producing accurate posterior samples by using HF numerical solvers in the second stage. We demonstrate the effectiveness of this algorithm for a range of problems, including linear and nonlinear Bayesian inverse problems with in-silico data and experimental data. The proposed algorithm is shown to seamlessly integrate with various low-fidelity and HF models, priors, and datasets. Remarkably, our proposed method outperforms the traditional HMC algorithm in both computational and statistical efficiency by several orders of magnitude, all while retaining or improving the accuracy in computed posterior statistics.

Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods have aimed to approximate Koopman operators while preserving key structures. However, approximating Koopman operators typically requires a dictionary of observables to capture the system's behavior in a finite-dimensional subspace. The selection of these functions is often heuristic, may result in the loss of spectral information, and can severely complicate structure preservation. This paper introduces Multiplicative Dynamic Mode Decomposition (MultDMD), which enforces the multiplicative structure inherent in the Koopman operator within its finite-dimensional approximation. Leveraging this multiplicative property, we guide the selection of observables and define a constrained optimization problem for the matrix approximation, which can be efficiently solved. MultDMD presents a structured approach to finite-dimensional approximations and can more accurately reflect the spectral properties of the Koopman operator. We elaborate on the theoretical framework of MultDMD, detailing its formulation, optimization strategy, and convergence properties. The efficacy of MultDMD is demonstrated through several examples, including the nonlinear pendulum, the Lorenz system, and fluid dynamics data, where we demonstrate its remarkable robustness to noise.

Pre-trained large language models (LLM) have emerged as a powerful tool for simulating various scenarios and generating output given specific instructions and multimodal input. In this work, we analyze the specific use of LLM to enhance a classical supervised machine learning method for classification problems. We propose a few approaches to integrate LLM into a classical machine learning estimator to further enhance the prediction performance. We examine the performance of the proposed approaches through both standard supervised learning binary classification tasks, and a transfer learning task where the test data observe distribution changes compared to the training data. Numerical experiments using four publicly available datasets are conducted and suggest that using LLM to enhance classical machine learning estimators can provide significant improvement on prediction performance.

Phishing email attacks are among the most common and most harmful cybersecurity attacks. With the emergence of generative AI, phishing attacks can be based on emails generated automatically, making it more difficult to detect them. That is, instead of a single email format sent to a large number of recipients, generative AI can be used to send each potential victim a different email, making it more difficult for cybersecurity systems to identify the scam email before it reaches the recipient. Here we describe a corpus of AI-generated phishing emails. We also use different machine learning tools to test the ability of automatic text analysis to identify AI-generated phishing emails. The results are encouraging, and show that machine learning tools can identify an AI-generated phishing email with high accuracy compared to regular emails or human-generated scam email. By applying descriptive analytic, the specific differences between AI-generated emails and manually crafted scam emails are profiled, and show that AI-generated emails are different in their style from human-generated phishing email scams. Therefore, automatic identification tools can be used as a warning for the user. The paper also describes the corpus of AI-generated phishing emails that is made open to the public, and can be used for consequent studies. While the ability of machine learning to detect AI-generated phishing email is encouraging, AI-generated phishing emails are different from regular phishing emails, and therefore it is important to train machine learning systems also with AI-generated emails in order to repel future phishing attacks that are powered by generative AI.

Non-parametric models, such as Gaussian Processes (GP), show promising results in the analysis of complex data. Their applications in neuroscience data have recently gained traction. In this research, we introduce a novel neural decoder model built upon GP models. The core idea is that two GPs generate neural data and their associated labels using a set of low-dimensional latent variables. Under this modeling assumption, the latent variables represent the underlying manifold or essential features present in the neural data. When GPs are trained, the latent variable can be inferred from neural data to decode the labels with a high accuracy. We demonstrate an application of this decoder model in a verbal memory experiment dataset and show that the decoder accuracy in predicting stimulus significantly surpasses the state-of-the-art decoder models. The preceding performance of this model highlights the importance of utilizing non-parametric models in the analysis of neuroscience data.

Discovering features that set elite players apart is of great significance for eSports coaches as it enables them to arrange a more effective training program focused on improving those features. Moreover, finding such features results in a better evaluation of eSports players skills, which, besides coaches, is of interest for game developers to design games automatically adaptable to the players expertise. Sensor data combined with machine learning have already proved effective in classifying eSports players. However, the existing methods do not provide sufficient information about features that distinguish high-skilled players. In this paper, we propose an efficient method to find these features and then use them to classify players' skill levels. We first apply a time window to extract the players' sensor data, including heart rate, hand activities, etc., before and after game events in the League of Legends game. We use the extracted segments and symbolic transfer entropy to calculate connectivity features between sensors. The most relevant features are then selected using the newly developed consensus nested cross validation method. These features, representing the harmony between body parts, are finally used to find the optimum window size and classify players' skills. The classification results demonstrate a significant improvement by achieving 90.1% accuracy. Also, connectivity features between players gaze positions and keyboard, mouse, and hand activities were the most distinguishing features in classifying players' skills. The proposed method in this paper can be similarly applied to sportspeople data and potentially revolutionize the training programs in both eSports and sports industries

We investigate trends in the data-error scaling behavior of machine learning (ML) models trained on discrete combinatorial spaces that are prone-to-mutation, such as proteins or organic small molecules. We trained and evaluated kernel ridge regression machines using variable amounts of computationally generated training data. Our synthetic datasets comprise i) two na\"ive functions based on many-body theory; ii) binding energy estimates between a protein and a mutagenised peptide; and iii) solvation energies of two 6-heavy atom structural graphs. In contrast to typical data-error scaling, our results showed discontinuous monotonic phase transitions during learning, observed as rapid drops in the test error at particular thresholds of training data. We observed two learning regimes, which we call saturated and asymptotic decay, and found that they are conditioned by the level of complexity (i.e. number of mutations) enclosed in the training set. We show that during training on this class of problems, the predictions were clustered by the ML models employed in the calibration plots. Furthermore, we present an alternative strategy to normalize learning curves (LCs) and the concept of mutant based shuffling. This work has implications for machine learning on mutagenisable discrete spaces such as chemical properties or protein phenotype prediction, and improves basic understanding of concepts in statistical learning theory.