Related papers: The Power of Many Samples in Query Complexity
Differential privacy is a notion of privacy that has become very popular in the database community. Roughly, the idea is that a randomized query mechanism provides sufficient privacy protection if the ratio between the probabilities that…
We introduce a theoretical framework for understanding and predicting the complexity of sequence classification tasks, using a novel extension of the theory of Boolean function sensitivity. The sensitivity of a function, given a…
Consider a class $\mH$ of binary functions $h: X\to\{-1, +1\}$ on a finite interval $X=[0, B]\subset \Real$. Define the {\em sample width} of $h$ on a finite subset (a sample) $S\subset X$ as $\w_S(h) \equiv \min_{x\in S} |\w_h(x)|$, where…
Smooth boosters generate distributions that do not place too much weight on any given example. Originally introduced for their noise-tolerant properties, such boosters have also found applications in differential privacy, reproducibility,…
We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…
We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…
A natural model of read-once linear branching programs is a branching program where queries are $\mathbb{F}_2$ linear forms, and along each path, the queries are linearly independent. We consider two restrictions of this model, which we…
A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives. These domains have been studied extensively in social choice theory due to both its practical importance and theoretical…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
Boolean function $F(x,y)$ for $x,y \in \{0,1\}^n$ is an XOR function if $F(x,y)=f(x\oplus y)$ for some function $f$ on $n$ input bits, where $\oplus$ is a bit-wise XOR. XOR functions are relevant in communication complexity, partially for…
Deep Neural Networks are known to be brittle to even minor distribution shifts compared to the training distribution. While one line of work has demonstrated that Simplicity Bias (SB) of DNNs - bias towards learning only the simplest…
In classification problems, the purpose of feature selection is to identify a small, highly discriminative subset of the original feature set. In many applications, the dataset may have thousands of features and only a few dozens of samples…
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
We study the effect that the amount of correlation in a bipartite distribution has on the communication complexity of a problem under that distribution. We introduce a new family of complexity measures that interpolates between the two…
In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$. The observations $y_i \in \mathbb{R}$ are thereby supposed to follow a noisy single-index…
We study distribution testing in the standard access model and the conditional access model when the memory available to the testing algorithm is bounded. In both scenarios, the samples appear in an online fashion and the goal is to test…
Let $X,X_1,X_2,\cdots$ be independent real valued random variables with a common distribution function $F$, and consider $\{X_1,\cdots,X_N \}$, possibly a big concrete data set, or an imaginary random sample of size $N\geq 1$ on $X$. In the…