相关论文: Three Costs of Amortizing Gaussian Process Inferen…

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…

We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with…

Many tasks in explainable machine learning, such as data valuation and feature attribution, perform expensive computation for each data point and are intractable for large datasets. These methods require efficient approximations, and…

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

A key task in AutoML is to model learning curves of machine learning models jointly as a function of model hyper-parameters and training progression. While Gaussian processes (GPs) are suitable for this task, na\"ive GPs require…

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…

Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a…

Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…

Modern learning systems increasingly rely on amortized learning - the idea of reusing computation or inductive biases shared across tasks to enable rapid generalization to novel problems. This principle spans a range of approaches,…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…

The accurate predictions and principled uncertainty measures provided by GP regression incur O(n^3) cost which is prohibitive for modern-day large-scale applications. This has motivated extensive work on computationally efficient…

We propose an efficient framework for amortized conditional inference by leveraging exact conditional score-guided diffusion models to train a non-reversible neural network as a conditional generative model. Traditional normalizing flow…

Causal sensitivity analysis aims to provide bounds for causal effect estimates in the presence of unobserved confounding. However, existing methods for causal sensitivity analysis are per-instance procedures, meaning that changes to the…