arXiv subjects

Renato Ferreira Pinto Jr.

Publications and source records attributed to Renato Ferreira Pinto Jr..

8 recordsLinked to original sources

arXiv2026

Distribution-Free Halfspace Testing with Samples

We prove a tight $Θ(n/ε)$ lower bound on the number of samples required for testing halfspaces over $\mathbb{R}^n$, in the distribution-free sample-based model where the underlying probability distribution is unknown to the algorithm, and the algorithm only receives random samples (i.e., it cannot make queries). This shows that testing is no more efficient than learning for halfspaces. We also show a matching upper bound for one-sided testers, improving on the standard (two-sided) testing-by-learning reduction, establishing that two-sided halfspace testers in this model have no advantage over one-sided testers.

cs.DS↗

arXiv2026

Learning and Testing Convex Functions

We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and testability have largely been examined only in discrete or restricted settings -- typically with respect to the Hamming distance, which is ill-suited for real-valued functions. In contrast, we study these problems in high dimensions under the standard Gaussian measure, assuming sample access to the function and a mild smoothness condition, namely Lipschitzness. A smoothness assumption is natural and, in fact, necessary even in one dimension: without it, convexity cannot be inferred from finitely many samples. As our main results, we give: - Learning Convex Functions: An agnostic proper learning algorithm for Lipschitz convex functions that achieves error $\varepsilon$ using $n^{O(1/\varepsilon^2)}$ samples, together with a complementary lower bound of $n^{\mathrm{poly}(1/\varepsilon)}$ samples in the \emph{correlational statistical query (CSQ)} model. - Testing Convex Functions: A tolerant (two-sided) tester for convexity of Lipschitz functions with the same sample complexity (as a corollary of our learning result), and a one-sided tester (which never rejects convex functions) using $O(\sqrt{n}/\varepsilon)^n$ samples.

cs.DS↗

arXiv2026

Testing Support Size More Efficiently Than Learning Histograms

Consider two problems about an unknown probability distribution $p$: 1. How many samples from $p$ are required to test if $p$ is supported on $n$ elements or not? Specifically, given samples from $p$, determine whether it is supported on at most $n$ elements, or it is "$ε$-far" (in total variation distance) from being supported on $n$ elements. 2. Given $m$ samples from $p$, what is the largest lower bound on its support size that we can produce? The best known upper bound for problem (1) uses a general algorithm for learning the histogram of the distribution $p$, which requires $Θ(\tfrac{n}{ε^2 \log n})$ samples. We show that testing can be done more efficiently than learning the histogram, using only $O(\tfrac{n}{ε\log n} \log(1/ε))$ samples, nearly matching the best known lower bound of $Ω(\tfrac{n}{ε\log n})$. This algorithm also provides a better solution to problem (2), producing larger lower bounds on support size than what follows from previous work. The proof relies on an analysis of Chebyshev polynomial approximations outside the range where they are designed to be good approximations, and the paper is intended as an accessible self-contained exposition of the Chebyshev polynomial method.

cs.DS↗

arXiv2026

Computational Complexity in Property Testing

We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity, relatively little is known about the computational hardness of property testers. Our goal is to chart the landscape of time-query interplay and develop tools for proving time complexity lower bounds. Our first contribution is a pair of time-query hierarchy theorems for property testing. For all suitable nondecreasing functions $q(n)$ and $t(n)$ with $t(n)\geq q(n)$, we construct properties with query complexity $\tildeΘ(q(n))$ and time complexity $\tildeΩ(t(n))$. Our weak hierarchy holds unconditionally, whereas the strong version-assuming the Strong Exponential Time Hypothesis-provides better control over the time complexity of the constructed properties. We then turn to halfspaces in $\mathbb{R}^d$, a fundamental class in property testing and learning theory. We study the problem of approximating the distance from the input function to the nearest halfspace within additive error $ε$. For the distribution-free distance approximation problem, known algorithms achieve query complexity $O(d/ε^2)$, but take time $\tildeΘ(1/ε^d)$. We provide a fine-grained justification for this gap: assuming the $k$-SUM conjecture, any algorithm must have running time $Ω(1/ε^{d/2})$. This fine-grained lower bound yields a provable separation between query and time complexity for a natural and well-studied (tolerant) testing problem. We also prove that any Statistical Query (SQ) algorithm under the standard Gaussian distribution requires $(1/ε)^{Ω(d)}$ queries if the queries are answered with additive error up to $ε^{Ω(d)}$, revealing a fundamental barrier even in the distribution-specific setting.

cs.CC↗

arXiv2023

Distribution Testing with a Confused Collector

We are interested in testing properties of distributions with systematically mislabeled samples. Our goal is to make decisions about unknown probability distributions, using a sample that has been collected by a confused collector, such as a machine-learning classifier that has not learned to distinguish all elements of the domain. The confused collector holds an unknown clustering of the domain and an input distribution $μ$, and provides two oracles: a sample oracle which produces a sample from $μ$ that has been labeled according to the clustering; and a label-query oracle which returns the label of a query point $x$ according to the clustering. Our first set of results shows that identity, uniformity, and equivalence of distributions can be tested efficiently, under the earth-mover distance, with remarkably weak conditions on the confused collector, even when the unknown clustering is adversarial. This requires defining a variant of the distribution testing task (inspired by the recent testable learning framework of Rubinfeld & Vasilyan), where the algorithm should test a joint property of the distribution and its clustering. As an example, we get efficient testers when the distribution tester is allowed to reject if it detects that the confused collector clustering is "far" from being a decision tree. The second set of results shows that we can sometimes do significantly better when the clustering is random instead of adversarial. For certain one-dimensional random clusterings, we show that uniformity can be tested under the TV distance using $\widetilde O\left(\frac{\sqrt n}{ρ^{3/2} ε^2}\right)$ samples and zero queries, where $ρ\in (0,1]$ controls the "resolution" of the clustering. We improve this to $O\left(\frac{\sqrt n}{ρε^2}\right)$ when queries are allowed.

cs.DS↗

arXiv2023

Distribution Testing Under the Parity Trace

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution testing to these problems, we introduce distribution testing under the parity trace, where the algorithm receives an ordered sample $S$ that reveals only the least significant bit of each element. This abstraction reveals connections between the following three problems of interest, allowing new upper and lower bounds: 1. In distribution testing with a confused collector, the collector of the sample may be incapable of distinguishing between nearby elements of a domain (e.g. a machine learning classifier). We prove bounds for distribution testing with a confused collector on domains structured as a cycle or a path. 2. Recent work on the fundamental testing vs. learning question established tight lower bounds on distribution-free sample-based property testing by reduction from distribution testing, but the tightness is limited to symmetric properties. The parity trace allows a broader family of equivalences to non-symmetric properties, while recovering and strengthening many of the previous results with a different technique. 3. We give the first results for property testing in the well-studied trace reconstruction model, where the goal is to test whether an unknown string $x$ satisfies some property or is far from satisfying that property, given only independent random traces of $x$. Our main technical result is a tight bound of $\widetilde Θ\left((n/ε)^{4/5} + \sqrt n/ε^2\right)$ for testing uniformity of distributions over $[n]$ under the parity trace, leading also to results for the problems above.

cs.DS↗

arXiv2020

VC Dimension and Distribution-Free Sample-Based Testing

We consider the problem of determining which classes of functions can be tested more efficiently than they can be learned, in the distribution-free sample-based model that corresponds to the standard PAC learning setting. Our main result shows that while VC dimension by itself does not always provide tight bounds on the number of samples required to test a class of functions in this model, it can be combined with a closely-related variant that we call "lower VC" (or LVC) dimension to obtain strong lower bounds on this sample complexity. We use this result to obtain strong and in many cases nearly optimal lower bounds on the sample complexity for testing unions of intervals, halfspaces, intersections of halfspaces, polynomial threshold functions, and decision trees. Conversely, we show that two natural classes of functions, juntas and monotone functions, can be tested with a number of samples that is polynomially smaller than the number of samples required for PAC learning. Finally, we also use the connection between VC dimension and property testing to establish new lower bounds for testing radius clusterability and testing feasibility of linear constraint systems.

cs.LG↗

arXiv2020

Text-based inference of moral sentiment change

We present a text-based framework for investigating moral sentiment change of the public via longitudinal corpora. Our framework is based on the premise that language use can inform people's moral perception toward right or wrong, and we build our methodology by exploring moral biases learned from diachronic word embeddings. We demonstrate how a parameter-free model supports inference of historical shifts in moral sentiment toward concepts such as slavery and democracy over centuries at three incremental levels: moral relevance, moral polarity, and fine-grained moral dimensions. We apply this methodology to visualizing moral time courses of individual concepts and analyzing the relations between psycholinguistic variables and rates of moral sentiment change at scale. Our work offers opportunities for applying natural language processing toward characterizing moral sentiment change in society.

cs.CL↗