Search Results for author:
Found 48 papers, 11 papers with code
Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization
In this paper, we study the problem of estimating the normalizing constant $\int e^{-\lambda f(x)}dx$ through queries to the black-box function $f$, where $f$ belongs to a reproducing kernel Hilbert space (RKHS), and $\lambda$ is a problem parameter.
Concomitant Group Testing
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item.
Communication-Constrained Bandits under Additive Gaussian Noise
We study a distributed stochastic multi-armed bandit where a client supplies the learner with communication-constrained feedback based on the rewards for the corresponding arm pulls.
Regret Bounds for Noise-Free Cascaded Kernelized Bandits
We consider optimizing a function network in the noise-free grey-box setting with RKHS function classes, where the exact intermediate results are observable.
Benefits of Monotonicity in Safe Exploration with Gaussian Processes
We consider the problem of sequentially maximising an unknown function over a set of actions while ensuring that every sampled point has a function value below a given safety threshold.
Max-Quantile Grouped Infinite-Arm Bandits
In this paper, we consider a bandit problem in which there are a number of groups each consisting of infinitely many arms.
Theoretical Perspectives on Deep Learning Methods in Inverse Problems
In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution.
Generative Principal Component Analysis
We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.
On Average-Case Error Bounds for Kernel-Based Bayesian Quadrature
In this paper, we study error bounds for {\em Bayesian quadrature} (BQ), with an emphasis on noisy settings, randomized algorithms, and average-case performance measures.
Improved Convergence Rates for Sparse Approximation Methods in Kernel-Based Learning
Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization.
A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits
We consider the sequential optimization of an unknown, continuous, and expensive to evaluate reward function, from noisy and adversarially corrupted observed rewards.
Max-Min Grouped Bandits
In this paper, we introduce a multi-armed bandit problem termed max-min grouped bandits, in which the arms are arranged in possibly-overlapping groups, and the goal is to find the group whose worst arm has the highest mean reward.
Open Problem: Tight Online Confidence Intervals for RKHS Elements
Confidence intervals are a crucial building block in the analysis of various online learning problems.
Adversarial Attacks on Gaussian Process Bandits
We focus primarily on targeted attacks on the popular GP-UCB algorithm and a related elimination-based algorithm, based on adversarially perturbing the function $f$ to produce another function $\tilde{f}$ whose optima are in some target region $\mathcal{R}_{\rm target}$.
Gaussian Process Bandit Optimization with Few Batches
In addition, in the case of a constant number of batches (not depending on $T$), we propose a modified version of our algorithm, and characterize how the regret is impacted by the number of batches, focusing on the squared exponential and Mat\'ern kernels.
Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors
In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector.
Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors
We also adapt this result to sparse phase retrieval, and show that $O(s \log n)$ samples are sufficient for a similar guarantee when the underlying signal is $s$-sparse and $n$-dimensional, matching an information-theoretic lower bound.
Lenient Regret and Good-Action Identification in Gaussian Process Bandits
In this paper, we study the problem of Gaussian process (GP) bandits under relaxed optimization criteria stating that any function value above a certain threshold is "good enough".
High-Dimensional Bayesian Optimization via Tree-Structured Additive Models
In addition, we propose a novel zooming-based algorithm that permits generalized additive models to be employed more efficiently in the case of continuous domains.
On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimization
In a robust setting in which every sampled point may be perturbed by a suitably-constrained adversary, we provide a novel lower bound for deterministic strategies, demonstrating an inevitable joint dependence of the cumulative regret on the corruption level and the time horizon, in contrast with existing lower bounds that only characterize the individual dependencies.
Stochastic Linear Bandits Robust to Adversarial Attacks
We consider a stochastic linear bandit problem in which the rewards are not only subject to random noise, but also adversarial attacks subject to a suitable budget $C$ (i. e., an upper bound on the sum of corruption magnitudes across the time horizon).
The Generalized Lasso with Nonlinear Observations and Generative Priors
We make the assumption of sub-Gaussian measurements, which is satisfied by a wide range of measurement models, such as linear, logistic, 1-bit, and other quantized models.
Corruption-Tolerant Gaussian Process Bandit Optimization
We consider the problem of optimizing an unknown (typically non-convex) function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS), based on noisy bandit feedback.
Learning Gaussian Graphical Models via Multiplicative Weights
Graphical model selection in Markov random fields is a fundamental problem in statistics and machine learning.
Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors
The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector.
Tight Regret Bounds for Noisy Optimization of a Brownian Motion
We consider the problem of Bayesian optimization of a one-dimensional Brownian motion in which the $T$ adaptively chosen observations are corrupted by Gaussian noise.
Learning Erdos-Renyi Random Graphs via Edge Detecting Queries
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes.
A Characteristic Function Approach to Deep Implicit Generative Modeling
In this paper, we formulate the problem of learning an IGM as minimizing the expected distance between characteristic functions.
Sample Complexity Lower Bounds for Compressive Sensing with Generative Models
The goal of standard compressive sensing is to estimate an unknown vector from linear measurements under the assumption of sparsity in some basis.
Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models
It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model.
Learning Erdős-Rényi Random Graphs via Edge Detecting Queries
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes.
Group Testing: An Information Theory Perspective
The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items.
Information Theory Discrete Mathematics Information Theory Probability Statistics Theory Statistics Theory
Support Recovery in the Phase Retrieval Model: Information-Theoretic Fundamental Limits
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations.
An Introductory Guide to Fano's Inequality with Applications in Statistical Estimation
Information theory plays an indispensable role in the development of algorithm-independent impossibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning.
Adversarially Robust Optimization with Gaussian Processes
In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even after this perturbation.
Tight Regret Bounds for Bayesian Optimization in One Dimension
We consider the problem of Bayesian optimization (BO) in one dimension, under a Gaussian process prior and Gaussian sampling noise.
Learning-Based Compressive MRI
In the area of magnetic resonance imaging (MRI), an extensive range of non-linear reconstruction algorithms have been proposed that can be used with general Fourier subsampling patterns.
High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups
In this paper, we consider the approach of Kandasamy et al. (2015), in which the high-dimensional function decomposes as a sum of lower-dimensional functions on subsets of the underlying variables.
Phase Transitions in the Pooled Data Problem
In this paper, we study the pooled data problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool.
Robust Submodular Maximization: A Non-Uniform Partitioning Approach
We study the problem of maximizing a monotone submodular function subject to a cardinality constraint $k$, with the added twist that a number of items $\tau$ from the returned set may be removed.
Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization
For the isotropic squared-exponential kernel in $d$ dimensions, we find that an average simple regret of $\epsilon$ requires $T = \Omega\big(\frac{1}{\epsilon^2} (\log\frac{1}{\epsilon})^{d/2}\big)$, and the average cumulative regret is at least $\Omega\big( \sqrt{T(\log T)^{d/2}} \big)$, thus matching existing upper bounds up to the replacement of $d/2$ by $2d+O(1)$ in both cases.
Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation
We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion.
Lower Bounds on Active Learning for Graphical Model Selection
We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active learning setting.
On the Difficulty of Selecting Ising Models with Approximate Recovery
We adopt an \emph{approximate recovery} criterion that allows for a number of missed edges or incorrectly-included edges, in contrast with the widely-studied exact recovery problem.
Partial Recovery Bounds for the Sparse Stochastic Block Model
In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities $\frac{a}{n}$ and $\frac{b}{n}$ respectively.
Time-Varying Gaussian Process Bandit Optimization
We illustrate the performance of the algorithms on both synthetic and real data, and we find the gradual forgetting of TV-GP-UCB to perform favorably compared to the sharp resetting of R-GP-UCB.
Learning-based Compressive Subsampling
In this paper, we instead take a principled learning-based approach in which a \emph{fixed} index set is chosen based on a set of training signals $\mathbf{x}_1,\dotsc,\mathbf{x}_m$.
Limits on Support Recovery with Probabilistic Models: An Information-Theoretic Framework
In several cases, our bounds not only provide matching scaling laws in the necessary and sufficient number of measurements, but also sharp thresholds with matching constant factors.
