Guy Blanc
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View article: The power of quantum circuits in sampling
The power of quantum circuits in sampling Open
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 cir…
View article: Computational-Statistical Tradeoffs from NP-hardness
Computational-Statistical Tradeoffs from NP-hardness Open
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 assumpt…
View article: Adaptive and oblivious statistical adversaries are equivalent
Adaptive and oblivious statistical adversaries are equivalent Open
We resolve a fundamental question about the ability to perform a statistical task, such as learning, when an adversary corrupts the sample. Such adversaries are specified by the types of corruption they can make and their level of knowledg…
View article: The Sample Complexity of Smooth Boosting and the Tightness of the Hardcore Theorem
The Sample Complexity of Smooth Boosting and the Tightness of the Hardcore Theorem Open
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, …
View article: A Strong Direct Sum Theorem for Distributional Query Complexity
A Strong Direct Sum Theorem for Distributional Query Complexity Open
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 $μ^k$. One strategy is to sequentially compute each of the $k$ copies t…
View article: Harnessing the Power of Choices in Decision Tree Learning
Harnessing the Power of Choices in Decision Tree Learning Open
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 …
View article: A Strong Composition Theorem for Junta Complexity and the Boosting of Property Testers
A Strong Composition Theorem for Junta Complexity and the Boosting of Property Testers Open
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 in…
View article: Lifting uniform learners via distributional decomposition
Lifting uniform learners via distributional decomposition Open
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…
View article: Subsampling Suffices for Adaptive Data Analysis
Subsampling Suffices for Adaptive Data Analysis Open
Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down …
View article: Certification with an NP Oracle
Certification with an NP Oracle Open
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…
View article: Multitask Learning via Shared Features: Algorithms and Hardness
Multitask Learning via Shared Features: Algorithms and Hardness Open
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 polyno…
View article: A Query-Optimal Algorithm for Finding Counterfactuals
A Query-Optimal Algorithm for Finding Counterfactuals Open
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 \[ {S(f)^{O(Δ_f(x^\star))}\cdot \log d}\] qu…
View article: Open Problem: Properly learning decision trees in polynomial time?
Open Problem: Properly learning decision trees in polynomial time? Open
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 n)…
View article: Popular decision tree algorithms are provably noise tolerant
Popular decision tree algorithms are provably noise tolerant Open
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, …
View article: Multiway Online Correlated Selection
Multiway Online Correlated Selection Open
We give a $0.5368$-competitive algorithm for edge-weighted online bipartite matching. Prior to our work, the best competitive ratio was $0.5086$ due to Fahrbach, Huang, Tao, and Zadimoghaddam (FOCS 2020). They achieved their breakthrough r…
View article: The Query Complexity of Certification
The Query Complexity of Certification Open
We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly mo…
View article: On Testing Decision Tree
On Testing Decision Tree Open
In this paper, we study testing decision tree of size and depth that are significantly smaller than the number of attributes n. Our main result addresses the problem of poly(n,1/ε) time algorithms with poly(s,1/ε) query complexity (indepen…
View article: On the power of adaptivity in statistical adversaries
On the power of adaptivity in statistical adversaries Open
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 cor…
View article: Provably efficient, succinct, and precise explanations
Provably efficient, succinct, and precise explanations Open
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an e…
View article: Decision tree heuristics can fail, even in the smoothed setting
Decision tree heuristics can fail, even in the smoothed setting Open
Greedy decision tree learning heuristics are mainstays of machine learning practice, but theoretical justification for their empirical success remains elusive. In fact, it has long been known that there are simple target functions for whic…
View article: Learning stochastic decision trees
Learning stochastic decision trees Open
We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an $η$-corrupted set of uniform random samples labeled by a size-$s$ stochastic decision tree, our algo…
View article: Decision Tree Heuristics Can Fail, Even in the Smoothed Setting
Decision Tree Heuristics Can Fail, Even in the Smoothed Setting Open
Greedy decision tree learning heuristics are mainstays of machine learning practice, but theoretical justification for their empirical success remains elusive. In fact, it has long been known that there are simple target functions for whic…
View article: Decision Tree Heuristics Can Fail, Even in the Smoothed Setting
Decision Tree Heuristics Can Fail, Even in the Smoothed Setting Open
Greedy decision tree learning heuristics are mainstays of machine learning practice, but theoretical justification for their empirical success remains elusive. In fact, it has long been known that there are simple target functions for whic…
View article: Learning Stochastic Decision Trees
Learning Stochastic Decision Trees Open
We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an η-corrupted set of uniform random samples labeled by a size-s stochastic decision tree, our algorith…
View article: Testing and reconstruction via decision trees.
Testing and reconstruction via decision trees. Open
We study sublinear and local computation algorithms for decision trees, focusing on testing and reconstruction. Our first result is a tester that runs in $\mathrm{poly}(\log s, 1/\varepsilon)\cdot n\log n$ time, makes $\mathrm{poly}(\log s…
View article: Reconstructing decision trees
Reconstructing decision trees Open
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: $\circ$ $T$ ha…
View article: Estimating decision tree learnability with polylogarithmic sample complexity
Estimating decision tree learnability with polylogarithmic sample complexity Open
We show that top-down decision tree learning heuristics are amenable to highly efficient learnability estimation: for monotone target functions, the error of the decision tree hypothesis constructed by these heuristics can be estimated wit…
View article: Query strategies for priced information, revisited
Query strategies for priced information, revisited Open
We consider the problem of designing query strategies for priced information, introduced by Charikar et al. In this problem the algorithm designer is given a function $f : \{0,1\}^n \to \{-1,1\}$ and a price associated with each of the $n$…
View article: Universal guarantees for decision tree induction via a higher-order splitting criterion
Universal guarantees for decision tree induction via a higher-order splitting criterion Open
We propose a simple extension of top-down decision tree learning heuristics such as ID3, C4.5, and CART. Our algorithm achieves provable guarantees for all target functions $f: \{-1,1\}^n \to \{-1,1\}$ with respect to the uniform distribut…
View article: Efficient hyperparameter optimization by way of PAC-Bayes bound minimization
Efficient hyperparameter optimization by way of PAC-Bayes bound minimization Open
Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently develo…