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  1. Article: Dispersion of free-falling saliva droplets by two-dimensional vortical flows.

    Avni, Orr / Dagan, Yuval

    Theoretical and computational fluid dynamics

    2022  Volume 36, Issue 6, Page(s) 993–1011

    Language English
    Publishing date 2022-11-05
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 1463179-9
    ISSN 1432-2250 ; 0935-4964
    ISSN (online) 1432-2250
    ISSN 0935-4964
    DOI 10.1007/s00162-022-00633-y
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  2. Book ; Online: From External to Swap Regret 2.0

    Dagan, Yuval / Daskalakis, Constantinos / Fishelson, Maxwell / Golowich, Noah

    An Efficient Reduction and Oblivious Adversary for Large Action Spaces

    2023  

    Abstract: We provide a novel reduction from swap-regret minimization to external-regret minimization, which improves upon the classical reductions of Blum-Mansour [BM07] and Stolz-Lugosi [SL05] in that it does not require finiteness of the space of actions. We ... ...

    Abstract We provide a novel reduction from swap-regret minimization to external-regret minimization, which improves upon the classical reductions of Blum-Mansour [BM07] and Stolz-Lugosi [SL05] in that it does not require finiteness of the space of actions. We show that, whenever there exists a no-external-regret algorithm for some hypothesis class, there must also exist a no-swap-regret algorithm for that same class. For the problem of learning with expert advice, our result implies that it is possible to guarantee that the swap regret is bounded by {\epsilon} after $\log(N)^{O(1/\epsilon)}$ rounds and with $O(N)$ per iteration complexity, where $N$ is the number of experts, while the classical reductions of Blum-Mansour and Stolz-Lugosi require $O(N/\epsilon^2)$ rounds and at least $\Omega(N^2)$ per iteration complexity. Our result comes with an associated lower bound, which -- in contrast to that in [BM07] -- holds for oblivious and $\ell_1$-constrained adversaries and learners that can employ distributions over experts, showing that the number of rounds must be $\tilde\Omega(N/\epsilon^2)$ or exponential in $1/\epsilon$. Our reduction implies that, if no-regret learning is possible in some game, then this game must have approximate correlated equilibria, of arbitrarily good approximation. This strengthens the folklore implication of no-regret learning that approximate coarse correlated equilibria exist. Importantly, it provides a sufficient condition for the existence of correlated equilibrium which vastly extends the requirement that the action set is finite, thus answering a question left open by [DG22; Ass+23]. Moreover, it answers several outstanding questions about equilibrium computation and learning in games.
    Keywords Computer Science - Machine Learning ; Computer Science - Artificial Intelligence ; Computer Science - Computer Science and Game Theory
    Subject code 005
    Publishing date 2023-10-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: Consistent Diffusion Models

    Daras, Giannis / Dagan, Yuval / Dimakis, Alexandros G. / Daskalakis, Constantinos

    Mitigating Sampling Drift by Learning to be Consistent

    2023  

    Abstract: Imperfect score-matching leads to a shift between the training and the sampling distribution of diffusion models. Due to the recursive nature of the generation process, errors in previous steps yield sampling iterates that drift away from the training ... ...

    Abstract Imperfect score-matching leads to a shift between the training and the sampling distribution of diffusion models. Due to the recursive nature of the generation process, errors in previous steps yield sampling iterates that drift away from the training distribution. Yet, the standard training objective via Denoising Score Matching (DSM) is only designed to optimize over non-drifted data. To train on drifted data, we propose to enforce a \emph{consistency} property which states that predictions of the model on its own generated data are consistent across time. Theoretically, we show that if the score is learned perfectly on some non-drifted points (via DSM) and if the consistency property is enforced everywhere, then the score is learned accurately everywhere. Empirically we show that our novel training objective yields state-of-the-art results for conditional and unconditional generation in CIFAR-10 and baseline improvements in AFHQ and FFHQ. We open-source our code and models: https://github.com/giannisdaras/cdm

    Comment: 29 pages, 8 figures
    Keywords Computer Science - Machine Learning ; Computer Science - Artificial Intelligence ; Computer Science - Computer Vision and Pattern Recognition ; Computer Science - Information Theory
    Subject code 006
    Publishing date 2023-02-17
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Online Learning and Solving Infinite Games with an ERM Oracle

    Assos, Angelos / Attias, Idan / Dagan, Yuval / Daskalakis, Constantinos / Fishelson, Maxwell

    2023  

    Abstract: While ERM suffices to attain near-optimal generalization error in the stochastic learning setting, this is not known to be the case in the online learning setting, where algorithms for general concept classes rely on computationally inefficient oracles ... ...

    Abstract While ERM suffices to attain near-optimal generalization error in the stochastic learning setting, this is not known to be the case in the online learning setting, where algorithms for general concept classes rely on computationally inefficient oracles such as the Standard Optimal Algorithm (SOA). In this work, we propose an algorithm for online binary classification setting that relies solely on ERM oracle calls, and show that it has finite regret in the realizable setting and sublinearly growing regret in the agnostic setting. We bound the regret in terms of the Littlestone and threshold dimensions of the underlying concept class. We obtain similar results for nonparametric games, where the ERM oracle can be interpreted as a best response oracle, finding the best response of a player to a given history of play of the other players. In this setting, we provide learning algorithms that only rely on best response oracles and converge to approximate-minimax equilibria in two-player zero-sum games and approximate coarse correlated equilibria in multi-player general-sum games, as long as the game has a bounded fat-threshold dimension. Our algorithms apply to both binary-valued and real-valued games and can be viewed as providing justification for the wide use of double oracle and multiple oracle algorithms in the practice of solving large games.

    Comment: In COLT2023
    Keywords Computer Science - Machine Learning ; Computer Science - Artificial Intelligence ; Computer Science - Computer Science and Game Theory ; Statistics - Machine Learning
    Subject code 006
    Publishing date 2023-07-04
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: EM's Convergence in Gaussian Latent Tree Models

    Dagan, Yuval / Daskalakis, Constantinos / Kandiros, Anthimos Vardis

    2022  

    Abstract: We study the optimization landscape of the log-likelihood function and the convergence of the Expectation-Maximization (EM) algorithm in latent Gaussian tree models, i.e. tree-structured Gaussian graphical models whose leaf nodes are observable and non- ... ...

    Abstract We study the optimization landscape of the log-likelihood function and the convergence of the Expectation-Maximization (EM) algorithm in latent Gaussian tree models, i.e. tree-structured Gaussian graphical models whose leaf nodes are observable and non-leaf nodes are unobservable. We show that the unique non-trivial stationary point of the population log-likelihood is its global maximum, and establish that the expectation-maximization algorithm is guaranteed to converge to it in the single latent variable case. Our results for the landscape of the log-likelihood function in general latent tree models provide support for the extensive practical use of maximum likelihood based-methods in this setting. Our results for the EM algorithm extend an emerging line of work on obtaining global convergence guarantees for this celebrated algorithm. We show our results for the non-trivial stationary points of the log-likelihood by arguing that a certain system of polynomial equations obtained from the EM updates has a unique non-trivial solution. The global convergence of the EM algorithm follows by arguing that all trivial fixed points are higher-order saddle points.
    Keywords Computer Science - Machine Learning ; Mathematics - Statistics Theory ; Statistics - Machine Learning
    Subject code 006 ; 519
    Publishing date 2022-11-21
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Book ; Online: Smoothed Online Learning is as Easy as Statistical Learning

    Block, Adam / Dagan, Yuval / Golowich, Noah / Rakhlin, Alexander

    2022  

    Abstract: Much of modern learning theory has been split between two regimes: the classical offline setting, where data arrive independently, and the online setting, where data arrive adversarially. While the former model is often both computationally and ... ...

    Abstract Much of modern learning theory has been split between two regimes: the classical offline setting, where data arrive independently, and the online setting, where data arrive adversarially. While the former model is often both computationally and statistically tractable, the latter requires no distributional assumptions. In an attempt to achieve the best of both worlds, previous work proposed the smooth online setting where each sample is drawn from an adversarially chosen distribution, which is smooth, i.e., it has a bounded density with respect to a fixed dominating measure. We provide tight bounds on the minimax regret of learning a nonparametric function class, with nearly optimal dependence on both the horizon and smoothness parameters. Furthermore, we provide the first oracle-efficient, no-regret algorithms in this setting. In particular, we propose an oracle-efficient improper algorithm whose regret achieves optimal dependence on the horizon and a proper algorithm requiring only a single oracle call per round whose regret has the optimal horizon dependence in the classification setting and is sublinear in general. Both algorithms have exponentially worse dependence on the smoothness parameter of the adversary than the minimax rate. We then prove a lower bound on the oracle complexity of any proper learning algorithm, which matches the oracle-efficient upper bounds up to a polynomial factor, thus demonstrating the existence of a statistical-computational gap in smooth online learning. Finally, we apply our results to the contextual bandit setting to show that if a function class is learnable in the classical setting, then there is an oracle-efficient, no-regret algorithm for contextual bandits in the case that contexts arrive in a smooth manner.
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning
    Subject code 006
    Publishing date 2022-02-09
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Book ; Online: A bounded-noise mechanism for differential privacy

    Dagan, Yuval / Kur, Gil

    2020  

    Abstract: Answering multiple counting queries is one of the best-studied problems in differential privacy. Its goal is to output an approximation of the average $\frac{1}{n}\sum_{i=1}^n \vec{x}^{(i)}$ of vectors $\vec{x}^{(i)} \in [0,1]^k$, while preserving the ... ...

    Abstract Answering multiple counting queries is one of the best-studied problems in differential privacy. Its goal is to output an approximation of the average $\frac{1}{n}\sum_{i=1}^n \vec{x}^{(i)}$ of vectors $\vec{x}^{(i)} \in [0,1]^k$, while preserving the privacy with respect to any $\vec{x}^{(i)}$. We present an $(\epsilon,\delta)$-private mechanism with optimal $\ell_\infty$ error for most values of $\delta$. This result settles the conjecture of Steinke and Ullman [2020] for the these values of $\delta$. Our algorithm adds independent noise of bounded magnitude to each of the $k$ coordinates, while prior solutions relied on unbounded noise such as the Laplace and Gaussian mechanisms.
    Keywords Computer Science - Data Structures and Algorithms ; Computer Science - Cryptography and Security ; Computer Science - Machine Learning
    Publishing date 2020-12-07
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Book ; Online: Majorizing Measures, Sequential Complexities, and Online Learning

    Block, Adam / Dagan, Yuval / Rakhlin, Sasha

    2021  

    Abstract: We introduce the technique of generic chaining and majorizing measures for controlling sequential Rademacher complexity. We relate majorizing measures to the notion of fractional covering numbers, which we show to be dominated in terms of sequential ... ...

    Abstract We introduce the technique of generic chaining and majorizing measures for controlling sequential Rademacher complexity. We relate majorizing measures to the notion of fractional covering numbers, which we show to be dominated in terms of sequential scale-sensitive dimensions in a horizon-independent way, and, under additional complexity assumptions establish a tight control on worst-case sequential Rademacher complexity in terms of the integral of sequential scale-sensitive dimension. Finally, we establish a tight contraction inequality for worst-case sequential Rademacher complexity. The above constitutes the resolution of a number of outstanding open problems in extending the classical theory of empirical processes to the sequential case, and, in turn, establishes sharp results for online learning.
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning
    Publishing date 2021-02-02
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Book ; Online: PAC learning with stable and private predictions

    Dagan, Yuval / Feldman, Vitaly

    2019  

    Abstract: We study binary classification algorithms for which the prediction on any point is not too sensitive to individual examples in the dataset. Specifically, we consider the notions of uniform stability (Bousquet and Elisseeff, 2001) and prediction privacy ( ... ...

    Abstract We study binary classification algorithms for which the prediction on any point is not too sensitive to individual examples in the dataset. Specifically, we consider the notions of uniform stability (Bousquet and Elisseeff, 2001) and prediction privacy (Dwork and Feldman, 2018). Previous work on these notions shows how they can be achieved in the standard PAC model via simple aggregation of models trained on disjoint subsets of data. Unfortunately, this approach leads to a significant overhead in terms of sample complexity. Here we demonstrate several general approaches to stable and private prediction that either eliminate or significantly reduce the overhead. Specifically, we demonstrate that for any class $C$ of VC dimension $d$ there exists a $\gamma$-uniformly stable algorithm for learning $C$ with excess error $\alpha$ using $\tilde O(d/(\alpha\gamma) + d/\alpha^2)$ samples. We also show that this bound is nearly tight. For $\epsilon$-differentially private prediction we give two new algorithms: one using $\tilde O(d/(\alpha^2\epsilon))$ samples and another one using $\tilde O(d^2/(\alpha\epsilon) + d/\alpha^2)$ samples. The best previously known bounds for these problems are $O(d/(\alpha^2\gamma))$ and $O(d/(\alpha^3\epsilon))$, respectively.
    Keywords Computer Science - Machine Learning ; Computer Science - Cryptography and Security ; Computer Science - Data Structures and Algorithms ; Statistics - Machine Learning
    Subject code 006
    Publishing date 2019-11-24
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Book ; Online: Score-Guided Intermediate Layer Optimization

    Daras, Giannis / Dagan, Yuval / Dimakis, Alexandros G. / Daskalakis, Constantinos

    Fast Langevin Mixing for Inverse Problems

    2022  

    Abstract: We prove fast mixing and characterize the stationary distribution of the Langevin Algorithm for inverting random weighted DNN generators. This result extends the work of Hand and Voroninski from efficient inversion to efficient posterior sampling. In ... ...

    Abstract We prove fast mixing and characterize the stationary distribution of the Langevin Algorithm for inverting random weighted DNN generators. This result extends the work of Hand and Voroninski from efficient inversion to efficient posterior sampling. In practice, to allow for increased expressivity, we propose to do posterior sampling in the latent space of a pre-trained generative model. To achieve that, we train a score-based model in the latent space of a StyleGAN-2 and we use it to solve inverse problems. Our framework, Score-Guided Intermediate Layer Optimization (SGILO), extends prior work by replacing the sparsity regularization with a generative prior in the intermediate layer. Experimentally, we obtain significant improvements over the previous state-of-the-art, especially in the low measurement regime.

    Comment: Accepted to ICML 2022. 32 pages, 9 Figures
    Keywords Computer Science - Machine Learning ; Computer Science - Artificial Intelligence
    Publishing date 2022-06-17
    Publishing country us
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