Extends linear classification framework to nonlinear SVM-based ranking problems.
problem Maximizing performance on relevant samples in ranking problems.
method Dualization, kernel addition, componentwise dual ascent method.
result General framework for nonlinear classifiers in ranking problems.
Kernel test evaluates dynamical system data streams.
problem Evaluate if data streams from dynamical systems are from the same distribution.
method Proposes a novel kernel two-sample test for dynamical systems, addressing independence and autocorrelation challenges.
result Data-driven method with theoretical guarantees for anomaly detection.
Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating human expertise remains elusive; for example, Gaussian processes with standard kerne…
A novel GP architecture, Thin and Deep GP, learns lower-dimensional representations without losing interpretability.
problem Challenges in selecting appropriate kernel for Gaussian processes.
method Proposes a novel synthesis of deep and shallow GP approaches, parameterizing lengthscale in a way that maintains interpretability and learns lower-dimensional embeddings.
result TDGP discovers lower-dimensional manifolds in input data, performs well in benchmark datasets, and behaves well with increasing layers.
New GP kernel handles mixed-categorical data, improving model accuracy.
problem Improving Gaussian process models for mixed-categorical data.
method Extends continuous exponential kernels to handle mixed-categorical variables.
result The proposed GP model gives higher likelihood and smaller residual error.
We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space embeddings, namely the ``Double Sum'' (DS) kernels recently considered in Bayesian set opt…
End-to-end graph SVM with graph convolutions and RKHS.
problem Graph classification with complex feature spaces.
method End-to-end training of graph convolutions, kernel function, and SVM parameters.
result Outperforms existing deep learning models on graph classification tasks.
Enhanced kernel framework for advanced data forecasting.
problem Complex mechanical behaviors and timefrequency dynamics in aircraft systems.
method Frequency-aware surrogate modeling with SMT kernels, extending kernel types and incorporating derivatives.
result Improved accuracy in forecasting CO2 concentrations and airline passenger traffic.
Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an unsupervised method …
New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.
problem Capturing complex spatiotemporal dependencies in Gaussian processes.
method Hybrid spectral method based on the harmonic oscillator, deriving explicit covariance kernels.
result Explicit non-separable covariance kernels with space-time interactions.
Kernel methods accurately predict Hamiltonian systems from data.
problem Data-driven simulation of Hamiltonian systems.
method Two-step and one-step kernel-based methods for identifying and forecasting Hamiltonian systems.
result Framework achieves accurate, data-efficient predictions across various benchmark systems.
AEN-RBF kernel improves robustness in Bayesian optimization for complex systems.
problem Bayesian optimization struggles with outliers in RBF kernel, leading to poor performance.
method Proposes AEN-RBF kernel function, demonstrating improved robustness and convergence.
result The AEN-RBF kernel function reduces mean squared prediction error and improves convergence.
The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced class sizes. Typically, nonlinear kernels produce significantly higher classifica…
BOKE optimizes expensive functions with reduced computational costs.
problem High computational cost of Gaussian process-based Bayesian optimization.
method Kernel regression and density-based exploration integrated into confidence bounds.
result BOKE achieves global convergence and superior computational efficiency.
A new method discovers equations from data using Bayesian and kernel techniques.
problem Discovering equations from data is hard due to sparsity and noise.
method Kernel regression for function estimation and Bayesian spike-and-slab prior for uncertainty quantification.
result KBASS method outperforms state-of-the-art methods on benchmark tasks.
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different ti…
The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel models to successfully tackle large-scale learning problems that are so far only …
LMGPs enable efficient, accurate data fusion across multiple data sources.
problem Data fusion across multi-fidelity data sources in engineering design.
method Latent-map Gaussian processes (LMGPs) for efficient and accurate data fusion.
result LMGPs provide increased accuracy, reduced costs, and flexibility to fuse any number of data sources.
Optimal kernel learning improves GP regression for high-dimensional inputs.
problem High computational costs and low prediction accuracy in GP models with many inputs.
method Approximates GP covariance with a convex combination of kernel functions, identifying active variables.
result Improves prediction accuracy and correctly identifies active input variables.
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data. Estimating such signals in all vertices given noisy observations of their values…
Safe Bayesian optimization tackles safety constraints in control engineering.
problem Handling safety constraints in parameter tuning of control systems.
method Lipschitz-only Safe Bayesian Optimization (LoSBO) and LoS-GP-UCB.
result SafeBO algorithms can violate safety constraints due to unreliable uncertainty bounds.
Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date, little work has been done to investigate the tradeoff between computational resourc…
Cellular network configuration plays a critical role in network performance. In current practice, network configuration depends heavily on field experience of engineers and often remains static for a long period of time. This practice is far from optimal. To address this limitation, online-learning-based approaches hav…
Study identifies unique minimizers for interaction kernels in particle systems.
problem Identifying unique interaction kernels in mean-field equations of interacting particles.
method Data-adaptive L2 spaces, RKHS analysis, regularization. result Characterization of identifiability in both finite and infinite particle systems.
WE constructs GP kernels for mixed inputs using weighted EDMs.
problem Limitation of standard GP models in handling categorical variables.
method WEGP constructs kernel function using weighted EDMs for categorical inputs.
result WEGP improves GP model accuracy in both synthetic and real-world optimization problems.
Paper uses SLT to improve model selection for SHM.
problem Model selection for SHM using data-based systems.
method Utilizes Statistical Learning Theory to rigorously estimate generalisation.
result Incorporating domain knowledge improves model generalisation.
Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian to recover the connected components. We study the performance of spectral clust…
Exact Gaussian Processes for massive datasets using non-stationary sparsity-discovering kernels.
problem High computational and storage costs for exact GPs in large datasets.
method Develop non-stationary kernels that allow the GP to discover sparse structure naturally.
result Exact Gaussian Processes scalable to over 5 million data points.
New method ensures consistent inference across different tensor parallel sizes for large language models.
problem Non-deterministic inference in large language models due to inconsistent reduction orders across GPUs.
method Tree-Based Invariant Kernels (TBIK) that align intra- and inter-GPU reduction orders through a unified hierarchical binary tree structure.
result Bit-wise identical results across different tensor parallel sizes for RL training.
KineticSim: A lightweight, high-performance execution engine for real-time market simulators
problem Simulating financial markets at scale with multi-agent models
method Reusable parallel design pattern: persistent, state-carrying clearing for iterative multi-agent reductions
result Reduces per-step critical-path depth from Theta(L+A) to Theta(log L + ceil(A/L))
Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this paper focuses on Bayesian inference of covariance (kernel) parameters using Mark…
Kernel-based GPs model continuous processes with uncountable information.
problem Uncountable information in Gaussian process modeling.
method Kernel-based approach using reproducing kernel Hilbert space.
result Proposed Gaussian process unifies finite and uncountable information.
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process is uncorrelated with its complex conjugate. This assumption is a good model of th…
PDE-DKL combines NNs and GPs for high-dimensional PDE problems.
problem High-dimensional PDE problems with scarce data.
method PDE-constrained Deep Kernel Learning (PDE-DKL) framework.
result High accuracy with reduced data requirements.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
Bayesian neural networks with Mercer priors for interpretable uncertainty quantification.
problem Uncertainty quantification in neural networks, especially for complex input-to-output mappings.
method Introducing Mercer priors for BNNs, which approximate a specified GP and are scalable.
result BNNs with Mercer priors can approximate the uncertainty of a specified GP, making them interpretable and scalable.
Gaussian process models simplify neural network behavior for easier understanding.
problem Understanding and predicting the behavior of deep learning systems.
method Constructing surrogate models using Gaussian processes from finite neural networks.
result Surrogate models capture phenomena like spectral bias and predict generalization well.
Tree ensemble kernels improve Bayesian optimization for mixed features and constraints.
problem Optimizing over mixed-feature spaces with known constraints.
method Kernel interpretation of tree ensembles as Gaussian Process prior, compatible optimization formulation for acquisition function, integration of known constraints.
result Framework outperforms state-of-the-art methods for mixed-feature spaces and constraints.
KineticSim accelerates financial market simulations 3406x over CPU.
problem Simulating financial markets at scale with multi-agent models is bottlenecked by sequential processing and GPU kernel overhead.
method Formalized and implemented a reusable parallel design pattern for iterative multi-agent reductions in thread-block shared memory.
result Achieved a peak throughput of over 54.7 billion agent-events per second, delivering 3406x speedup over CPU.
This review discusses challenges and solutions for AI in chemical engineering.
problem Challenges in applying classical machine learning to chemical engineering data.
method Identifying four data characteristics and discussing their applications and solutions.
result Current research extends data science and machine learning to handle chemical engineering data challenges.
The paper presents a method to infer unknown forcing functions in differential equations using Gaussian processes and adjoints.
problem Inferring unknown forcing functions in differential equations from noisy observations.
method Using adjoint methods to efficiently infer Gaussian process (GP) driven differential equations, with truncated basis expansions of the GP kernel.
result Efficient Bayesian inference of forcing functions modeled as GPs using adjoints, with lower computation than MCMC methods.
Optimal engine operation during a transient driving cycle is the key to achieving greater fuel economy, engine efficiency, and reduced emissions. In order to achieve continuously optimal engine operation, engine calibration methods use a combination of static correlations obtained from dynamometer tests for steady-stat…
Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or outliers which may result in a poor learner model in terms of generalization. This pa…
New method learns policies from offline data using operator models.
problem Limited understanding of approximation errors in offline reinforcement learning.
method Linking reinforcement learning to Hamilton-Jacobi-Bellman equation, proposing operator-theoretic algorithm.
result Global convergence of the value function and finite-sample guarantees derived.
ROME improves density estimation for multi-modal, non-normal data.
problem Robust multi-modal density estimation in non-normal, highly correlated distributions.
method ROME uses clustering to segment multi-modal data into uni-modal clusters, then combines KDE estimates for each cluster.
result ROME outperforms state-of-the-art methods and is more robust to various distributions.
Paper introduces novel survival models for handling censored data.
problem Complex data structures and heavy censoring in survival analysis.
method Combines imprecise probability theory with attention mechanisms.
result Proposed models, especially iSurvJ, outperform traditional methods.
Paper uses deep reinforcement learning for better control of rocket engines during start-up phases.
problem Lack of optimal control during transient phases of liquid rocket engines.
method Deep reinforcement learning approach for optimal control of a gas-generator engine's continuous start-up phase.
result Deep reinforcement learning controller achieves highest performance and minimal computational effort.
Paper proposes verifier engineering for improving foundation models.
problem Challenges in providing effective supervision signals for foundation models.
method Leverages automated verifiers to perform verification tasks and deliver feedback.
result Verifier engineering can enhance foundation models' capabilities.