Related papers: The Sample Complexity of Uniform Approximation for…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…
The one clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single input qubit is pure and all other input qubits are maximally mixed. In spite of the severe restriction, the model can solve several…
Selling a single item to $n$ self-interested buyers is a fundamental problem in economics, where the two objectives typically considered are welfare maximization and revenue maximization. Since the optimal mechanisms are often impractical…
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation…
Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum…
We study the task of high-dimensional entangled mean estimation in the subset-of-signals model. Specifically, given $N$ independent random points $x_1,\ldots,x_N$ in $\mathbb{R}^D$ and a parameter $\alpha \in (0, 1)$ such that each $x_i$ is…
In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field…
In this paper, we study the problem of distributed mean estimation with 1-bit communication constraints. We propose a mean estimator that is based on (randomized and sequentially-chosen) interval queries, whose 1-bit outcome indicates…
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…
Linear attention has attracted interest as a computationally efficient approximation to softmax attention, especially for long sequences. Recent studies have explored distilling softmax attention in pre-trained Transformers into linear…
Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the…
One of the most challenging issues in federated learning is that the data is often not independent and identically distributed (nonIID). Clients are expected to contribute the same type of data and drawn from one global distribution.…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
Uncertainty quantification is a critical aspect of reinforcement learning and deep learning, with numerous applications ranging from efficient exploration and stable offline reinforcement learning to outlier detection in medical…
In this paper, we investigate the sample complexity of policy evaluation in infinite-horizon offline reinforcement learning (also known as the off-policy evaluation problem) with linear function approximation. We identify a hard regime…
We investigate sample-based learning of conditional distributions on multi-dimensional unit boxes, allowing for different dimensions of the feature and target spaces. Our approach involves clustering data near varying query points in the…
We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbol{\alpha}\|_{\infty}^{2})$…
We consider the problem of computing a $k$-sparse approximation to the Fourier transform of a length $N$ signal. Our main result is a randomized algorithm for computing such an approximation (i.e. achieving the $\ell_2/\ell_2$ sparse…
We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. Replacing the indicator function in…