arXiv subjects

Patrick Thiran

Publications and source records attributed to Patrick Thiran.

At least 37 records · Page 2Linked to original sources

arXiv2024

Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization

Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ comprises high-dimensional factors.

cs.LG↗

arXiv2023

Momentum-Based Policy Gradient with Second-Order Information

Variance-reduced gradient estimators for policy gradient methods have been one of the main focus of research in the reinforcement learning in recent years as they allow acceleration of the estimation process. We propose a variance-reduced policy-gradient method, called SHARP, which incorporates second-order information into stochastic gradient descent (SGD) using momentum with a time-varying learning rate. SHARP algorithm is parameter-free, achieving $ε$-approximate first-order stationary point with $O(ε^{-3})$ number of trajectories, while using a batch size of $O(1)$ at each iteration. Unlike most previous work, our proposed algorithm does not require importance sampling which can compromise the advantage of variance reduction process. Moreover, the variance of estimation error decays with the fast rate of $O(1/t^{2/3})$ where $t$ is the number of iterations. Our extensive experimental evaluations show the effectiveness of the proposed algorithm on various control tasks and its advantage over the state of the art in practice.

cs.LG↗

arXiv2023

Differences Between Hard and Noisy-labeled Samples: An Empirical Study

Extracting noisy or incorrectly labeled samples from a labeled dataset with hard/difficult samples is an important yet under-explored topic. Two general and often independent lines of work exist, one focuses on addressing noisy labels, and another deals with hard samples. However, when both types of data are present, most existing methods treat them equally, which results in a decline in the overall performance of the model. In this paper, we first design various synthetic datasets with custom hardness and noisiness levels for different samples. Our proposed systematic empirical study enables us to better understand the similarities and more importantly the differences between hard-to-learn samples and incorrectly-labeled samples. These controlled experiments pave the way for the development of methods that distinguish between hard and noisy samples. Through our study, we introduce a simple yet effective metric that filters out noisy-labeled samples while keeping the hard samples. We study various data partitioning methods in the presence of label noise and observe that filtering out noisy samples from hard samples with this proposed metric results in the best datasets as evidenced by the high test accuracy achieved after models are trained on the filtered datasets. We demonstrate this for both our created synthetic datasets and for datasets with real-world label noise. Furthermore, our proposed data partitioning method significantly outperforms other methods when employed within a semi-supervised learning framework.

cs.LG↗

arXiv2023

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with $1\leα\le2$ which holds in a wide range of applications in machine learning and signal processing. This condition ensures that any first-order stationary point is a global optimum. We prove that the total sample complexity of SCRN in achieving $ε$-global optimum is $\mathcal{O}(ε^{-7/(2α)+1})$ for $1\leα< 3/2$ and $\mathcal{\tilde{O}}(ε^{-2/(α)})$ for $3/2\leα\le 2$. SCRN improves the best-known sample complexity of stochastic gradient descent. Even under a weak version of gradient dominance property, which is applicable to policy-based reinforcement learning (RL), SCRN achieves the same improvement over stochastic policy gradient methods. Additionally, we show that the average sample complexity of SCRN can be reduced to ${\mathcal{O}}(ε^{-2})$ for $α=1$ using a variance reduction method with time-varying batch sizes. Experimental results in various RL settings showcase the remarkable performance of SCRN compared to first-order methods.

cs.LG↗

arXiv2022

Leveraging Unlabeled Data to Track Memorization

Deep neural networks may easily memorize noisy labels present in real-world data, which degrades their ability to generalize. It is therefore important to track and evaluate the robustness of models against noisy label memorization. We propose a metric, called susceptibility, to gauge such memorization for neural networks. Susceptibility is simple and easy to compute during training. Moreover, it does not require access to ground-truth labels and it only uses unlabeled data. We empirically show the effectiveness of our metric in tracking memorization on various architectures and datasets and provide theoretical insights into the design of the susceptibility metric. Finally, we show through extensive experiments on datasets with synthetic and real-world label noise that one can utilize susceptibility and the overall training accuracy to distinguish models that maintain a low memorization on the training set and generalize well to unseen clean data.

cs.LG↗

arXiv2021

The power of adaptivity in source identification with time queries on the path

We study the problem of identifying the source of a stochastic diffusion process spreading on a graph based on the arrival times of the diffusion at a few queried nodes. In a graph $G=(V,E)$, an unknown source node $v^* \in V$ is drawn uniformly at random, and unknown edge weights $w(e)$ for $e\in E$, representing the propagation delays along the edges, are drawn independently from a Gaussian distribution of mean $1$ and variance $σ^2$. An algorithm then attempts to identify $v^*$ by querying nodes $q \in V$ and being told the length of the shortest path between $q$ and $v^*$ in graph $G$ weighted by $w$. We consider two settings: non-adaptive, in which all query nodes must be decided in advance, and adaptive, in which each query can depend on the results of the previous ones. Both settings are motivated by an application of the problem to epidemic processes (where the source is called patient zero), which we discuss in detail. We characterize the query complexity when $G$ is an $n$-node path. In the non-adaptive setting, $Θ(nσ^2)$ queries are needed for $σ^2 \leq 1$, and $Θ(n)$ for $σ^2 \geq 1$. In the adaptive setting, somewhat surprisingly, only $Θ(\log\log_{1/σ}n)$ are needed when $σ^2 \leq 1/2$, and $Θ(\log \log n)+O_σ(1)$ when $σ^2 \geq 1/2$. This is the first mathematical study of source identification with time queries in a non-deterministic diffusion process.

cs.DS↗

arXiv2021

Source Detection via Contact Tracing in the Presence of Asymptomatic Patients

Inferring the source of a diffusion in a large network of agents is a difficult but feasible task, if a few agents act as sensors revealing the time at which they got hit by the diffusion. A main limitation of current source detection algorithms is that they assume full knowledge of the contact network, which is rarely the case, especially for epidemics, where the source is called patient zero. Inspired by recent contact tracing algorithms, we propose a new framework, which we call Source Detection via Contact Tracing Framework (SDCTF). In the SDCTF, the source detection task starts at the time of the first hospitalization, and initially we have no knowledge about the contact network other than the identity of the first hospitalized agent. We may then explore the network by contact queries, and obtain symptom onset times by test queries in an adaptive way. We also assume that some of the agents may be asymptomatic, and therefore cannot reveal their symptom onset time. Our goal is to find patient zero with as few contact and test queries as possible. We propose two local search algorithms for the SDCTF: the LS algorithm is more data-efficient, but can fail to find the true source if many asymptomatic agents are present, whereas the LS+ algorithm is more robust to asymptomatic agents. By simulations we show that both LS and LS+ outperform state of the art adaptive and non-adaptive source detection algorithms adapted to the SDCTF, even though these baseline algorithms have full access to the contact network. Extending the theory of random exponential trees, we analytically approximate the probability of success of the LS/ LS+ algorithms, and we show that our analytic results match the simulations. Finally, we benchmark our algorithms on the Data-driven COVID-19 Simulator developed by Lorch et al., which is the first time source detection algorithms are tested on such a complex dataset.

cs.SI↗

arXiv2021

On the robustness of the metric dimension of grid graphs to adding a single edge

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to the graph. The extra edge can either be selected adversarially, in which case we are interested in the largest possible value that the MD can take, or uniformly at random, in which case we are interested in the distribution of the MD. The adversarial setting has already been studied by [Eroh et. al., 2015] for general graphs, who found an example where the MD doubles on adding a single edge. By constructing a different example, we show that this increase can be as large as exponential. However, we believe that such a large increase can occur only in specially constructed graphs, and that in most interesting graph families, the MD at most doubles on adding a single edge. We prove this for $d$-dimensional grid graphs, by showing that $2d$ appropriately chosen corners and the endpoints of the extra edge can distinguish every pair of nodes, no matter where the edge is added. For the special case of $d=2$, we show that it suffices to choose the four corners as landmarks. Finally, when the extra edge is sampled uniformly at random, we conjecture that the MD of 2-dimensional grids converges in probability to $3+\mathrm{Ber}(8/27)$, and we give an almost complete proof.

math.CO↗

arXiv2021

Sequential metric dimension for random graphs

In the localization game on a graph, the goal is to find a fixed but unknown target node $v^\star$ with the least number of distance queries possible. In the $j^{th}$ step of the game, the player queries a single node $v_j$ and receives, as an answer to their query, the distance between the nodes $v_j$ and $v^\star$. The sequential metric dimension (SMD) is the minimal number of queries that the player needs to guess the target with absolute certainty, no matter where the target is. The term SMD originates from the related notion of metric dimension (MD), which can be defined the same way as the SMD, except that the player's queries are non-adaptive. In this work, we extend the results of \cite{bollobas2012metric} on the MD of Erdős-Rényi graphs to the SMD. We find that, in connected Erdős-Rényi graphs, the MD and the SMD are a constant factor apart. For the lower bound we present a clean analysis by combining tools developed for the MD and a novel coupling argument. For the upper bound we show that a strategy that greedily minimizes the number of candidate targets in each step uses asymptotically optimal queries in Erdős-Rényi graphs. Connections with source localization, binary search on graphs and the birthday problem are discussed.

math.CO↗

arXiv2021

Disparity Between Batches as a Signal for Early Stopping

We propose a metric for evaluating the generalization ability of deep neural networks trained with mini-batch gradient descent. Our metric, called gradient disparity, is the $\ell_2$ norm distance between the gradient vectors of two mini-batches drawn from the training set. It is derived from a probabilistic upper bound on the difference between the classification errors over a given mini-batch, when the network is trained on this mini-batch and when the network is trained on another mini-batch of points sampled from the same dataset. We empirically show that gradient disparity is a very promising early-stopping criterion (i) when data is limited, as it uses all the samples for training and (ii) when available data has noisy labels, as it signals overfitting better than the validation data. Furthermore, we show in a wide range of experimental settings that gradient disparity is strongly related to the generalization error between the training and test sets, and that it is also very informative about the level of label noise.

cs.LG↗

arXiv2020

Generalization Comparison of Deep Neural Networks via Output Sensitivity

Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter by linking the loss function to the output's sensitivity to its input. We find a rather strong empirical relation between the output sensitivity and the variance in the bias-variance decomposition of the loss function, which hints on using sensitivity as a metric for comparing the generalization performance of networks, without requiring labeled data. We find that sensitivity is decreased by applying popular methods which improve the generalization performance of the model, such as (1) using a deep network rather than a wide one, (2) adding convolutional layers to baseline classifiers instead of adding fully-connected layers, (3) using batch normalization, dropout and max-pooling, and (4) applying parameter initialization techniques.

cs.LG↗

arXiv2019

A User Study of Perceived Carbon Footprint

We propose a statistical model to understand people's perception of their carbon footprint. Driven by the observation that few people think of CO2 impact in absolute terms, we design a system to probe people's perception from simple pairwise comparisons of the relative carbon footprint of their actions. The formulation of the model enables us to take an active-learning approach to selecting the pairs of actions that are maximally informative about the model parameters. We define a set of 18 actions and collect a dataset of 2183 comparisons from 176 users on a university campus. The early results reveal promising directions to improve climate communication and enhance climate mitigation.

stat.ML↗

arXiv2019

Learning Hawkes Processes from a Handful of Events

Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization. Our approach is able to optimize over an extended set of hyper-parameters. It is also able to take into account the uncertainty in the model parameters by learning a posterior distribution over them. Experimental results on both synthetic and real datasets show that our approach significantly outperforms state-of-the-art methods under short observation sequences.

cs.LG↗

arXiv2018

Coordinate Descent with Bandit Sampling

Coordinate descent methods usually minimize a cost function by updating a random decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest decrease in the cost function. However, finding this coordinate would require checking all of them, which would effectively negate the improvement in computational tractability that coordinate descent is intended to afford. To address this, we propose a new adaptive method for selecting a coordinate. First, we find a lower bound on the amount the cost function decreases when a coordinate is updated. We then use a multi-armed bandit algorithm to learn which coordinates result in the largest lower bound by interleaving this learning with conventional coordinate descent updates except that the coordinate is selected proportionately to the expected decrease. We show that our approach improves the convergence of coordinate descent methods both theoretically and experimentally.

cs.LG↗

arXiv2017

Stochastic Optimization with Bandit Sampling

Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertently slows down the convergence rate of the algorithms. One way to reduce this variance is to sample the datapoints from a carefully selected non-uniform distribution. In this work, we propose a novel non-uniform sampling approach that uses the multi-armed bandit framework. Theoretically, we show that our algorithm asymptotically approximates the optimal variance within a factor of 3. Empirically, we show that using this datapoint-selection technique results in a significant reduction in the convergence time and variance of several stochastic optimization algorithms such as SGD, SVRG and SAGA. This approach for sampling datapoints is general, and can be used in conjunction with any algorithm that uses an unbiased gradient estimation -- we expect it to have broad applicability beyond the specific examples explored in this work.

cs.LG↗

arXiv2017

Back to the Source: an Online Approach for Sensor Placement and Source Localization

Source localization, the act of finding the originator of a disease or rumor in a network, has become an important problem in sociology and epidemiology. The localization is done using the infection state and time of infection of a few designated sensor nodes; however, maintaining sensors can be very costly in practice. We propose the first online approach to source localization: We deploy a priori only a small number of sensors (which reveal if they are reached by an infection) and then iteratively choose the best location to place new sensors in order to localize the source. This approach allows for source localization with a very small number of sensors; moreover, the source can be found while the epidemic is still ongoing. Our method applies to a general network topology and performs well even with random transmission delays.

cs.SI↗

arXiv2016

Observer Placement for Source Localization: The Effect of Budgets and Transmission Variance

When an epidemic spreads in a network, a key question is where was its source, i.e., the node that started the epidemic. If we know the time at which various nodes were infected, we can attempt to use this information in order to identify the source. However, maintaining observer nodes that can provide their infection time may be costly, and we may have a budget $k$ on the number of observer nodes we can maintain. Moreover, some nodes are more informative than others due to their location in the network. Hence, a pertinent question arises: Which nodes should we select as observers in order to maximize the probability that we can accurately identify the source? Inspired by the simple setting in which the node-to-node delays in the transmission of the epidemic are deterministic, we develop a principled approach for addressing the problem even when transmission delays are random. We show that the optimal observer-placement differs depending on the variance of the transmission delays and propose approaches in both low- and high-variance settings. We validate our methods by comparing them against state-of-the-art observer-placements and show that, in both settings, our approach identifies the source with higher accuracy.

cs.SI↗

arXiv2016

How CSMA/CA With Deferral Affects Performance and Dynamics in Power-Line Communications

Power-line communications (PLC) are becoming a key component in home networking, because they provide easy and high-throughput connectivity. The dominant MAC protocol for high data-rate PLC, the IEEE 1901, employs a CSMA/CA mechanism similar to the backoff process of 802.11. Existing performance evaluation studies of this protocol assume that the backoff processes of the stations are independent (the so-called decoupling assumption). However, in contrast to 802.11, 1901 stations can change their state after sensing the medium busy, which is regulated by the so-called deferral counter. This mechanism introduces strong coupling between the stations and, as a result, makes existing analyses inaccurate. In this paper, we propose a performance model for 1901, which does not rely on the decoupling assumption. We prove that our model admits a unique solution for a wide range of configurations and confirm the accuracy of the model using simulations. Our results show that we outperform current models based on the decoupling assumption. In addition to evaluating the performance in steady state, we further study the transient dynamics of 1901, which is also affected by the deferral counter.

cs.NI↗