This study proposes a methodology to utilize machine learning (ML) for topology optimization of periodic lattice structures. In particular, we investigate data representation of lattice structures used as input data for ML models to improve the performance of the models, focusing on the filtering process and feature selection. We use the filtering technique to explicitly consider the connectivity of lattice members and perform feature selection to reduce the input data size. In addition, we propose a convolution approach to apply pre-trained models for small structures to structures of larger sizes. The computational cost for obtaining optimal topologies by a heuristic method is reduced by incorporating the prediction of the trained ML model into the optimization process. In the numerical examples, a response prediction model is constructed for a lattice structure of 4x4 units, and topology optimization of 4x4-unit and 8x8-unit structures is performed by simulated annealing assisted by the trained ML model. The example demonstrates that ML models perform higher accuracy by using the filtered data as input than by solely using the data representing the existence of each member. It is also demonstrated that a small-scale prediction model can be constructed with sufficient accuracy by feature selection. Additionally, the proposed method can find the optimal structure in less computation time than the pure simulated annealing.

Parametrised quantum circuits offer expressive and data-efficient representations for machine learning. Due to quantum states residing in a high-dimensional Hilbert space, parametrised quantum circuits have a natural interpretation in terms of kernel methods. The representation of quantum circuits in terms of quantum kernels has been studied widely in quantum supervised learning, but has been overlooked in the context of quantum reinforcement learning. This paper proposes parametric and non-parametric policy gradient and actor-critic algorithms with quantum kernel policies in quantum environments. This approach, implemented with both numerical and analytical quantum policy gradient techniques, allows exploiting the many advantages of kernel methods, including available analytic forms for the gradient of the policy and tunable expressiveness. The proposed approach is suitable for vector-valued action spaces and each of the formulations demonstrates a quadratic reduction in query complexity compared to their classical counterparts. Two actor-critic algorithms, one based on stochastic policy gradient and one based on deterministic policy gradient (comparable to the popular DDPG algorithm), demonstrate additional query complexity reductions compared to quantum policy gradient algorithms under favourable conditions.

Previous deep learning approaches for survival analysis have primarily relied on ranking losses to improve discrimination performance, which often comes at the expense of calibration performance. To address such an issue, we propose a novel contrastive learning approach specifically designed to enhance discrimination \textit{without} sacrificing calibration. Our method employs weighted sampling within a contrastive learning framework, assigning lower penalties to samples with similar survival outcomes. This aligns well with the assumption that patients with similar event times share similar clinical statuses. Consequently, when augmented with the commonly used negative log-likelihood loss, our approach significantly improves discrimination performance without directly manipulating the model outputs, thereby achieving better calibration. Experiments on multiple real-world clinical datasets demonstrate that our method outperforms state-of-the-art deep survival models in both discrimination and calibration. Through comprehensive ablation studies, we further validate the effectiveness of our approach through quantitative and qualitative analyses.

The multivariate Gaussian distribution underpins myriad operations-research, decision-analytic, and machine-learning models (e.g., Bayesian optimization, Gaussian influence diagrams, and variational autoencoders). However, despite recent advances in adversarial machine learning (AML), inference for Gaussian models in the presence of an adversary is notably understudied. Therefore, we consider a self-interested attacker who wishes to disrupt a decisionmaker's conditional inference and subsequent actions by corrupting a set of evidentiary variables. To avoid detection, the attacker also desires the attack to appear plausible wherein plausibility is determined by the density of the corrupted evidence. We consider white- and grey-box settings such that the attacker has complete and incomplete knowledge about the decisionmaker's underlying multivariate Gaussian distribution, respectively. Select instances are shown to reduce to quadratic and stochastic quadratic programs, and structural properties are derived to inform solution methods. We assess the impact and efficacy of these attacks in three examples, including, real estate evaluation, interest rate estimation and signals processing. Each example leverages an alternative underlying model, thereby highlighting the attacks' broad applicability. Through these applications, we also juxtapose the behavior of the white- and grey-box attacks to understand how uncertainty and structure affect attacker behavior.

We consider the problem of predicting perturbation effects via causal models. In many applications, it is a priori unknown which mechanisms of a system are modified by an external perturbation, even though the features of the perturbation are available. For example, in genomics, some properties of a drug may be known, but not their causal effects on the regulatory pathways of cells. We propose a generative intervention model (GIM) that learns to map these perturbation features to distributions over atomic interventions in a jointly-estimated causal model. Contrary to prior approaches, this enables us to predict the distribution shifts of unseen perturbation features while gaining insights about their mechanistic effects in the underlying data-generating process. On synthetic data and scRNA-seq drug perturbation data, GIMs achieve robust out-of-distribution predictions on par with unstructured approaches, while effectively inferring the underlying perturbation mechanisms, often better than other causal inference methods.

In this paper, we consider nonparametric clustering of $M$ independent and identically distributed (i.i.d.) data streams generated from unknown distributions. The distributions of the $M$ data streams belong to $K$ underlying distribution clusters. Existing results on exponentially consistent nonparametric clustering algorithms, like single linkage-based (SLINK) clustering and $k$-medoids distribution clustering, assume that the maximum intra-cluster distance ($d_L$) is smaller than the minimum inter-cluster distance ($d_H$). First, in the fixed sample size (FSS) setting, we show that exponential consistency can be achieved for SLINK clustering under a less strict assumption, $d_I < d_H$, where $d_I$ is the maximum distance between any two sub-clusters of a cluster that partition the cluster. Note that $d_I < d_L$ in general. Our results show that SLINK is exponentially consistent for a larger class of problems than $k$-medoids distribution clustering. We also identify examples where $k$-medoids clustering is unable to find the true clusters, but SLINK is exponentially consistent. Then, we propose a sequential clustering algorithm, named SLINK-SEQ, based on SLINK and prove that it is also exponentially consistent. Simulation results show that the SLINK-SEQ algorithm requires fewer expected number of samples than the FSS SLINK algorithm for the same probability of error.

Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on analytical accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC.Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.

Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language and then sample via Hamiltonian Monte Carlo (HMC). However, there are many ways a user can transform a model that make inference more or less efficient. In particular, marginalizing some variables can greatly improve inference but is difficult for users to do manually. We develop an algorithm to easily marginalize random effects in LMMs. A naive approach introduces cubic time operations within an inference algorithm like HMC, but we reduce the running time to linear using fast linear algebra techniques. We show that marginalization is always beneficial when applicable and highlight improvements in various models, especially ones from cognitive sciences.

Clustering complex data in the form of attributed graphs has attracted increasing attention, where appropriate graph representation is a critical prerequisite for accurate cluster analysis. However, the Graph Convolutional Network will homogenize the representation of graph nodes due to the well-known over-smoothing effect. This limits the network architecture to a shallow one, losing the ability to capture the critical global distribution information for clustering. Therefore, we propose a generalized graph auto-encoder network, which introduces quaternion operations to the encoders to achieve efficient structured feature representation learning without incurring deeper network and larger-scale parameters. The generalization of our method lies in the following two aspects: 1) connecting the quaternion operation naturally suitable for four feature components with graph data of arbitrary attribute dimensions, and 2) introducing a generalized graph clustering objective as a loss term to obtain clustering-friendly representations without requiring a pre-specified number of clusters $k$. It turns out that the representations of nodes learned by the proposed Graph Clustering based on Generalized Quaternion representation learning (GCGQ) are more discriminative, containing global distribution information, and are more general, suiting downstream clustering under different $k$s. Extensive experiments including significance tests, ablation studies, and qualitative results, illustrate the superiority of GCGQ. The source code is temporarily opened at \url{https://anonymous.4open.science/r/ICLR-25-No7181-codes}.

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models (GPSSMs) have recently gained significant attention due to their combination of flexibility and interpretability. However, for online learning, the field lacks an efficient method suitable for scenarios where prior information regarding data distribution and model function is limited. To address this issue, this paper proposes a recursive GPSSM method with adaptive capabilities for both operating domains and Gaussian process (GP) hyperparameters. Specifically, we first utilize first-order linearization to derive a Bayesian update equation for the joint distribution between the system state and the GP model, enabling closed-form and domain-independent learning. Second, an online selection algorithm for inducing points is developed based on informative criteria to achieve lightweight learning. Third, to support online hyperparameter optimization, we recover historical measurement information from the current filtering distribution. Comprehensive evaluations on both synthetic and real-world datasets demonstrate the superior accuracy, computational efficiency, and adaptability of our method compared to state-of-the-art online GPSSM techniques.