Li-Yang Tan
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…
We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…
A central question in computer science and statistics is whether efficient algorithms can achieve the information-theoretic limits of statistical problems. Many computational-statistical tradeoffs have been shown under average-case…
The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…
We connect the problem of properly PAC learning decision trees to the parameterized Nearest Codeword Problem ($k$-NCP). Despite significant effort by the respective communities, algorithmic progress on both problems has been stuck: the…
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 consider the task of properly PAC learning decision trees with queries. Recent work of Koch, Strassle, and Tan showed that the strictest version of this task, where the hypothesis tree $T$ is required to be optimally small, is NP-hard.…
Consider the expected query complexity of computing the $k$-fold direct product $f^{\otimes k}$ of a function $f$ to error $\varepsilon$ with respect to a distribution $\mu^k$. One strategy is to sequentially compute each of the $k$ copies…
We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These algorithms, which have been central to machine learning for decades, are greedy in nature: they…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
We prove a strong composition theorem for junta complexity and show how such theorems can be used to generically boost the performance of property testers. The $\varepsilon$-approximate junta complexity of a function $f$ is the smallest…
We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…
In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^\star$, and the goal is to find a certificate of size $\le \text{poly}(k)$ for $f$'s value at $x^\star$. This problem is in…
We establish new hardness results for decision tree optimization problems, adding to a line of work that dates back to Hyafil and Rivest in 1976. We prove, under randomized ETH, superpolynomial lower bounds for two basic problems: given an…
We investigate the computational efficiency of multitask learning of Boolean functions over the $d$-dimensional hypercube, that are related by means of a feature representation of size $k \ll d$ shared across all tasks. We present a…
We design an algorithm for finding counterfactuals with strong theoretical guarantees on its performance. For any monotone model $f : X^d \to \{0,1\}$ and instance $x^\star$, our algorithm makes \[ {S(f)^{O(\Delta_f(x^\star))}\cdot \log…
The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…
We study a fundamental question concerning adversarial noise models in statistical problems where the algorithm receives i.i.d. draws from a distribution $\mathcal{D}$. The definitions of these adversaries specify the type of allowable…
Using the framework of boosting, we prove that all impurity-based decision tree learning algorithms, including the classic ID3, C4.5, and CART, are highly noise tolerant. Our guarantees hold under the strongest noise model of nasty noise,…
We give the first {\sl reconstruction algorithm} for decision trees: given queries to a function $f$ that is $\mathrm{opt}$-close to a size-$s$ decision tree, our algorithm provides query access to a decision tree $T$ where: $\circ$ $T$ has…