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1. Properly Learning Decision Trees in almost Polynomial Time

   Blanc, Guy ; Lange, Jane ; Qiao, Mingda ; Tan, Li-Yang ( January 2022 , Journal of the Association for Computing Machinery)

   We give an nO(log log n)-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over { ± 1}n. Even in the realizable setting, the previous fastest runtime was nO(log n), a consequence of a classic algorithm of Ehrenfeucht and Haussler. Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of O’Donnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be “pruned” so that every variable in the resulting tree is influential. 

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2. Properly learning decision trees in almost polynomial time

   https://doi.org/10.1109/FOCS52979.2021.00093  

   Blanc, G. ; Lange, J. ; Qiao, M. ; Tan, L. ( January 2021 , Annual Symposium on Foundations of Computer Science)

   We give an nO(loglogn)-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over {±1}n. Even in the realizable setting, the previous fastest runtime was nO(logn), a consequence of a classic algorithm of Ehrenfeucht and Haussler. Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of O'Donnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be “pruned” so that every variable in the resulting tree is influential. 

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3. Smoothed Analysis of Information Spreading in Dynamic Networks

   Dinitz, Michael ; Fineman, Jeremy ; Gilbert, Seth ; Newport, Calvin ( October 2022 , Leibniz international proceedings in informatics)

   The best known solutions for k-message broadcast in dynamic networks of size n require Ω(nk) rounds. In this paper, we see if these bounds can be improved by smoothed analysis. To do so, we study perhaps the most natural randomized algorithm for disseminating tokens in this setting: at every time step, choose a token to broadcast randomly from the set of tokens you know. We show that with even a small amount of smoothing (i.e., one random edge added per round), this natural strategy solves k-message broadcast in Õ(n+k³) rounds, with high probability, beating the best known bounds for k = o(√n) and matching the Ω(n+k) lower bound for static networks for k = O(n^{1/3}) (ignoring logarithmic factors). In fact, the main result we show is even stronger and more general: given 𝓁-smoothing (i.e., 𝓁 random edges added per round), this simple strategy terminates in O(kn^{2/3}log^{1/3}(n)𝓁^{-1/3}) rounds. We then prove this analysis close to tight with an almost-matching lower bound. To better understand the impact of smoothing on information spreading, we next turn our attention to static networks, proving a tight bound of Õ(k√n) rounds to solve k-message broadcast, which is better than what our strategy can achieve in the dynamic setting. This confirms the intuition that although smoothed analysis reduces the difficulties induced by changing graph structures, it does not eliminate them altogether. Finally, we apply tools developed to support our smoothed analysis to prove an optimal result for k-message broadcast in so-called well-mixed networks in the absence of smoothing. By comparing this result to an existing lower bound for well-mixed networks, we establish a formal separation between oblivious and strongly adaptive adversaries with respect to well-mixed token spreading, partially resolving an open question on the impact of adversary strength on the k-message broadcast problem. 

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4. Predicting Facebook sentiments towards research

   https://doi.org/10.1016/j.nlp.2023.100010  

   Shahzad, Murtuza ; Freeman, Cole ; Rahimi, Mona ; Alhoori, Hamed ( June 2023 , Natural Language Processing Journal)

   Social media platforms provide users with various ways of interacting with each other, such as commenting, reacting to posts, sharing content, and uploading pictures. Facebook is one of the most popular platforms, and its users frequently share and reshare posts, including research articles. Moreover, the reactions feature on Facebook allows users to express their feelings towards the content they view, providing valuable data for analysis. This study aims to predict the emotional impact of Facebook posts relating to research articles. We collected data on Facebook posts related to various scientific research domains, including Health Sciences, Social Sciences, Dentistry, Arts, and Humanities. We observed Facebook users’ reactions towards research articles and posts and found that ‘Like’ reactions were the most common. We also noticed that research articles from the Dentistry research domain received a lot of ‘Haha’ reactions. We used machine learning models to predict the sentiment of Facebook posts related to research articles. We used features such as the research article’s title sentiment, abstract sentiment, abstract length, author count, and research domain to build the models. We used five classifiers: Random Forest, Decision Tree, K-Nearest Neighbors, Logistic Regression, and Naïve Bayes. The models were evaluated using accuracy, precision, recall, and F-1 score metrics. The Random Forest classifier was the best model for two- and three-class labels, achieving accuracy measures of 86% and 66%, respectively. We also evaluated the feature importance for the Random Forest model and found that the sentiment of the research article’s title is crucial in predicting the sentiment of the Facebook post. This study has substantial implications for public engagement in science-related messages. The emotional reactions of Facebook users towards research articles and posts can provide valuable insights into public engagement in science, and predicting the emotional impact of Facebook posts related to research articles can help researchers understand how the public perceives scientific research. The findings of the study can aid researchers in effectively communicating their research and engaging the public in scientific discourse. 

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5. Random Quantum Circuits Transform Local Noise into Global White Noise

   https://doi.org/10.1007/s00220-024-04958-z  

   Dalzell, Alexander M. ; Hunter-Jones, Nicholas ; Brandão, Fernando G. S. L. ( March 2024 , Communications in Mathematical Physics)

   We study the distribution over measurement outcomes of noisy random quantum circuits in the regime of low fidelity, which corresponds to the setting where the computation experiences at least one gate-level error with probability close to one. We model noise by adding a pair of weak, unital, single-qubit noise channels after each two-qubit gate, and we show that for typical random circuit instances, correlations between the noisy output distribution$$p_{\text {noisy}}$$$p_{\text{noisy}}$and the corresponding noiseless output distribution$$p_{\text {ideal}}$$$p_{\text{ideal}}$shrink exponentially with the expected number of gate-level errors. Specifically, the linear cross-entropy benchmarkFthat measures this correlation behaves as$$F=\text {exp}(-2s\epsilon \pm O(s\epsilon ^2))$$$F=\text{exp}(-2sϵ\pm O\left(s{ϵ}^2\right))$, where$$\epsilon $$$ϵ$is the probability of error per circuit location andsis the number of two-qubit gates. Furthermore, if the noise is incoherent—for example, depolarizing or dephasing noise—the total variation distance between the noisy output distribution$$p_{\text {noisy}}$$$p_{\text{noisy}}$and the uniform distribution$$p_{\text {unif}}$$$p_{\text{unif}}$decays at precisely the same rate. Consequently, the noisy output distribution can be approximated as$$p_{\text {noisy}}\approx Fp_{\text {ideal}}+ (1-F)p_{\text {unif}}$$$p_{\text{noisy}}\approx F{p}_{\text{ideal}}+(1-F)p_{\text{unif}}$. In other words, although at least one local error occurs with probability$$1-F$$$1-F$, the errors are scrambled by the random quantum circuit and can be treated as global white noise, contributing completely uniform output. Importantly, we upper bound the average total variation error in this approximation by$$O(F\epsilon \sqrt{s})$$$O\left(Fϵ\sqrt{s}\right)$. Thus, the “white-noise approximation” is meaningful when$$\epsilon \sqrt{s} \ll 1$$$ϵ\sqrt{s}\ll 1$, a quadratically weaker condition than the$$\epsilon s\ll 1$$$ϵs\ll 1$requirement to maintain high fidelity. The bound applies if the circuit size satisfies$$s \ge \Omega (n\log (n))$$$s\ge \Omega (nlog(n\left)\right)$, which corresponds to onlylogarithmic depthcircuits, and if, additionally, the inverse error rate satisfies$$\epsilon ^{-1} \ge {\tilde{\Omega }}(n)$$${ϵ}^{-1}\ge \tilde{\Omega }\left(n\right)$, which is needed to ensure errors are scrambled faster thanFdecays. The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; for example, it was an underlying assumption in complexity-theoretic arguments that noisy random quantum circuits cannot be efficiently sampled classically, even when the fidelity is low. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds.

    

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