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1. On the Complexity of Learning a Class Ratio from Unlabeled Data

   https://doi.org/10.1613/jair.1.12013  

   Fish, Benjamin; Reyzin, Lev (September 2020, Journal of Artificial Intelligence Research)

   In the problem of learning a class ratio from unlabeled data, which we call CR learning, the training data is unlabeled, and only the ratios, or proportions, of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls. In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of CR learning and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently CR learned is a strict subset of what can be learned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose CR learnability is independent of ZFC, the standard set theoretic axioms. This implies that CR learning cannot be easily characterized (like PAC by VC dimension). 

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2. Robust learning under clean-label attack

   Blum, A.; Hanneke, S.; Qian, J.; Shao, H. (January 2021, Conference on Learning Theory)

   Belkin, M.; Kpotufe, S. (Ed.)

   We study the problem of robust learning under clean-label data-poisoning attacks, where the at-tacker injects (an arbitrary set of) correctly-labeled examples to the training set to fool the algorithm into making mistakes on specific test instances at test time. The learning goal is to minimize the attackable rate (the probability mass of attackable test instances), which is more difficult than optimal PAC learning. As we show, any robust algorithm with diminishing attackable rate can achieve the optimal dependence on ε in its PAC sample complexity, i.e., O(1/ε). On the other hand, the attackable rate might be large even for some optimal PAC learners, e.g., SVM for linear classifiers. Furthermore, we show that the class of linear hypotheses is not robustly learnable when the data distribution has zero margin and is robustly learnable in the case of positive margin but requires sample complexity exponential in the dimension. For a general hypothesis class with bounded VC dimension, if the attacker is limited to add at most t >0 poison examples, the optimal robust learning sample complexity grows almost linearly with t. 

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3. Hardness of Learning Boolean Functions from Label Proportions

   https://doi.org/10.4230/LIPIcs.FSTTCS.2023.37  

   Guruswami, Venkatesan; Saket, Rishi (January 2023, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Bouyer, Patricia; Srinivasan, Srikanth (Ed.)

   In recent years the framework of learning from label proportions (LLP) has been gaining importance in machine learning. In this setting, the training examples are aggregated into subsets or bags and only the average label per bag is available for learning an example-level predictor. This generalizes traditional PAC learning which is the special case of unit-sized bags. The computational learning aspects of LLP were studied in recent works [R. Saket, 2021; R. Saket, 2022] which showed algorithms and hardness for learning halfspaces in the LLP setting. In this work we focus on the intractability of LLP learning Boolean functions. Our first result shows that given a collection of bags of size at most 2 which are consistent with an OR function, it is NP-hard to find a CNF of constantly many clauses which satisfies any constant-fraction of the bags. This is in contrast with the work of [R. Saket, 2021] which gave a (2/5)-approximation for learning ORs using a halfspace. Thus, our result provides a separation between constant clause CNFs and halfspaces as hypotheses for LLP learning ORs. Next, we prove the hardness of satisfying more than 1/2 + o(1) fraction of such bags using a t-DNF (i.e. DNF where each term has ≤ t literals) for any constant t. In usual PAC learning such a hardness was known [S. Khot and R. Saket, 2008] only for learning noisy ORs. We also study the learnability of parities and show that it is NP-hard to satisfy more than (q/2^{q-1} + o(1))-fraction of q-sized bags which are consistent with a parity using a parity, while a random parity based algorithm achieves a (1/2^{q-2})-approximation. 

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4. Active Tolerant Testing

   Blum, Avrim; Hu, Lunjia (January 2018, Proceedings of the 31st Conference On Learning Theory)

   In this work, we show that for a nontrivial hypothesis class C, we can estimate the distance of a target function f to C (estimate the error rate of the best h∈C) using substantially fewer labeled examples than would be needed to actually {\em learn} a good h∈C. Specifically, we show that for the class C of unions of d intervals on the line, in the active learning setting in which we have access to a pool of unlabeled examples drawn from an arbitrary underlying distribution D, we can estimate the error rate of the best h∈C to an additive error ϵ with a number of label requests that is {\em independent of d} and depends only on ϵ. In particular, we make O((1/ϵ^6)log(1/ϵ)) label queries to an unlabeled pool of size O((d/ϵ^2)log(1/ϵ)). This task of estimating the distance of an unknown f to a given class C is called {\em tolerant testing} or {\em distance estimation} in the testing literature, usually studied in a membership query model and with respect to the uniform distribution. Our work extends that of Balcan et al. (2012) who solved the {\em non}-tolerant testing problem for this class (distinguishing the zero-error case from the case that the best hypothesis in the class has error greater than ϵ). We also consider the related problem of estimating the performance of a given learning algorithm A in this setting. That is, given a large pool of unlabeled examples drawn from distribution D, can we, from only a few label queries, estimate how well A would perform if the entire dataset were labeled and given as training data to A? We focus on k-Nearest Neighbor style algorithms, and also show how our results can be applied to the problem of hyperparameter tuning (selecting the best value of k for the given learning problem). 

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5. Efficient Federated Domain Translation

   Zhou, Zeyu; Azam, Sheikh Shams; Brinton, Christopher; Inouye, David I. (January 2023, International Conference on Learning Representations)

   A central theme in federated learning (FL) is the fact that client data distributions are often not independent and identically distributed (IID), which has strong implications on the training process. While most existing FL algorithms focus on the conventional non-IID setting of class imbalance or missing classes across clients, in practice, the distribution differences could be more complex, e.g., changes in class conditional (domain) distributions. In this paper, we consider this complex case in FL wherein each client has access to only one domain distribution. For tasks such as domain generalization, most existing learning algorithms require access to data from multiple clients (i.e., from multiple domains) during training, which is prohibitive in FL. To address this challenge, we propose a federated domain translation method that generates pseudodata for each client which could be useful for multiple downstream learning tasks. We empirically demonstrate that our translation model is more resource-efficient (in terms of both communication and computation) and easier to train in an FL setting than standard domain translation methods. Furthermore, we demonstrate that the learned translation model enables use of state-of-the-art domain generalization methods in a federated setting, which enhances accuracy and robustness to increases in the synchronization period compared to existing methodology. 

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