arXiv subjects

Panos Toulis

Publications and source records attributed to Panos Toulis.

29 records · Page 2Linked to original sources

arXiv2020

The Proximal Robbins-Monro Method

The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general, and fast. However, standard stochastic approximations are often numerically unstable. Deterministic optimization, on the other hand, increasingly uses proximal updates to achieve numerical stability in a principled manner. A theoretical gap has thus emerged. While standard stochastic approximations are subsumed by the framework of Robbins and Monro (1951), there is no such framework for stochastic approximations with proximal updates. In this paper, we conceptualize a proximal version of the classical Robbins-Monro procedure. Our theoretical analysis demonstrates that the proposed procedure has important stability benefits over the classical Robbins-Monro procedure, while it retains the best known convergence rates. Exact implementations of the proximal Robbins-Monro procedure are challenging, but we show that approximate implementations lead to procedures that are easy to implement, and still dominate classical procedures by achieving numerical stability, practically without tradeoffs. Moreover, approximate proximal Robbins-Monro procedures can be applied even when the objective cannot be calculated analytically, and so they generalize stochastic proximal procedures currently in use.

math.ST↗

arXiv2018

Conditional randomization tests of causal effects with interference between units

Many causal questions involve interactions between units, also known as interference, for example between individuals in households, students in schools, or firms in markets. In this paper, we formalize the concept of a conditioning mechanism, which provides a framework for constructing valid and powerful randomization tests under general forms of interference. We describe our framework in the context of two-stage randomized designs and apply our approach to a randomized evaluation of an intervention targeting student absenteeism in the School District of Philadelphia. We show improvements over existing methods in terms of computational and statistical power.

stat.ME↗

arXiv2018

Convergence diagnostics for stochastic gradient descent with constant step size

Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure oscillates in that region, commonly around a single point. In this paper, we develop a statistical diagnostic test to detect such phase transition in the context of stochastic gradient descent with constant learning rate. We present theory and experiments suggesting that the region where the proposed diagnostic is activated coincides with the convergence region. For a class of loss functions, we derive a closed-form solution describing such region. Finally, we suggest an application to speed up convergence of stochastic gradient descent by halving the learning rate each time stationarity is detected. This leads to a new variant of stochastic gradient descent, which in many settings is comparable to state-of-art.

stat.ML↗

arXiv2018

Propensity score methodology in the presence of network entanglement between treatments

In experimental design and causal inference, it may happen that the treatment is not defined on individual experimental units, but rather on pairs or, more generally, on groups of units. For example, teachers may choose pairs of students who do not know each other to teach a new curriculum; regulators might allow or disallow merging of firms, and biologists may introduce or inhibit interactions between genes or proteins. In this paper, we formalize this experimental setting, and we refer to the individual treatments in such setting as entangled treatments. We then consider the special case where individual treatments depend on a common population quantity, and develop theory and methodology to deal with this case. In our target applications, the common population quantity is a network, and the individual treatments are defined as functions of the change in the network between two specific time points. Our focus is on estimating the causal effect of entangled treatments in observational studies where entangled treatments are endogenous and cannot be directly manipulated. When treatment cannot be manipulated, be it entangled or not, it is necessary to account for the treatment assignment mechanism to avoid selection bias, commonly through a propensity score methodology. In this paper, we quantify the extent to which classical propensity score methodology ignores treatment entanglement, and characterize the bias in the estimated causal effects. To characterize such bias we introduce a novel similarity function between propensity score models, and a practical approximation of it, which we use to quantify model misspecification of propensity scores due to entanglement. One solution to avoid the bias in the presence of entangled treatments is to model the change in the network, directly, and calculate an individual unit's propensity score by averaging treatment assignments over this change.

math.ST↗

arXiv2016

Asymptotic and finite-sample properties of estimators based on stochastic gradients

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradient descent procedures, which involve parameter updates that are implicitly defined. Intuitively, implicit updates shrink standard stochastic gradient descent updates. The amount of shrinkage depends on the observed Fisher information matrix, which does not need to be explicitly computed; thus, implicit procedures increase stability without increasing the computational burden. Our theoretical analysis provides the first full characterization of the asymptotic behavior of both standard and implicit stochastic gradient descent-based estimators, including finite-sample error bounds. Importantly, analytical expressions for the variances of these stochastic gradient-based estimators reveal their exact loss of efficiency. We also develop new algorithms to compute implicit stochastic gradient descent-based estimators for generalized linear models, Cox proportional hazards, M-estimators, in practice, and perform extensive experiments. Our results suggest that implicit stochastic gradient descent procedures are poised to become a workhorse for approximate inference from large data sets

stat.ME↗

arXiv2016

Towards stability and optimality in stochastic gradient descent

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient as estimators of the true parameter value. To address these two issues, we propose a new iterative procedure termed averaged implicit SGD (AI-SGD). For statistical efficiency, AI-SGD employs averaging of the iterates, which achieves the optimal Cramér-Rao bound under strong convexity, i.e., it is an optimal unbiased estimator of the true parameter value. For numerical stability, AI-SGD employs an implicit update at each iteration, which is related to proximal operators in optimization. In practice, AI-SGD achieves competitive performance with other state-of-the-art procedures. Furthermore, it is more stable than averaging procedures that do not employ proximal updates, and is simple to implement as it requires fewer tunable hyperparameters than procedures that do employ proximal updates.

stat.ME↗

arXiv2015

Stochastic gradient descent methods for estimation with large data sets

We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one iterate as a parameter estimate, and successively update that iterate based on a single data point. When the update is based on a noisy gradient, the stochastic approximation is known as standard stochastic gradient descent, which has been fundamental in modern applications with large data sets. Additionally, our methods are numerically stable because they employ implicit updates of the iterates. Intuitively, an implicit update is a shrinked version of a standard one, where the shrinkage factor depends on the observed Fisher information at the corresponding data point. This shrinkage prevents numerical divergence of the iterates, which can be caused either by excess noise or outliers. Our sgd package in R offers the most extensive and robust implementation of stochastic gradient descent methods. We demonstrate that sgd dominates alternative software in runtime for several estimation problems with massive data sets. Our applications include the wide class of generalized linear models as well as M-estimation for robust regression.

stat.CO↗

arXiv2015

Incentive-Compatible Experimental Design

We consider the design of experiments to evaluate treatments that are administered by self-interested agents, each seeking to achieve the highest evaluation and win the experiment. For example, in an advertising experiment, a company wishes to evaluate two marketing agents in terms of their efficacy in viral marketing, and assign a contract to the winner agent. Contrary to traditional experimental design, this problem has two new implications. First, the experiment induces a game among agents, where each agent can select from multiple versions of the treatment it administers. Second, the action of one agent -- selection of treatment version -- may affect the actions of another agent, with the resulting strategic interference complicating the evaluation of agents. An incentive-compatible experiment design is one with an equilibrium where each agent selects its natural action, which is the action that would maximize the performance of the agent if there was no competition (e.g., expected number of conversions if agent was assigned the contract). Under a general formulation of experimental design, we identify sufficient conditions that guarantee incentive-compatible experiments. These conditions rely on the existence of statistics that can estimate how agents would perform without competition, and their use in constructing score functions to evaluate the agents. In the setting with no strategic interference, we also study the power of the design, i.e., the probability that the best agent wins, and show how to improve the power of incentive-compatible designs. From the technical side, our theory uses a range of statistical methods such as hypothesis testing, variance-stabilizing transformations and the Delta method, all of which rely on asymptotics.

stat.ME↗

arXiv2014

Implicit Temporal Differences

In reinforcement learning, the TD($λ$) algorithm is a fundamental policy evaluation method with an efficient online implementation that is suitable for large-scale problems. One practical drawback of TD($λ$) is its sensitivity to the choice of the step-size. It is an empirically well-known fact that a large step-size leads to fast convergence, at the cost of higher variance and risk of instability. In this work, we introduce the implicit TD($λ$) algorithm which has the same function and computational cost as TD($λ$), but is significantly more stable. We provide a theoretical explanation of this stability and an empirical evaluation of implicit TD($λ$) on typical benchmark tasks. Our results show that implicit TD($λ$) outperforms standard TD($λ$) and a state-of-the-art method that automatically tunes the step-size, and thus shows promise for wide applicability.

stat.ML↗

arXiv2014

Long-term causal effects of economic mechanisms on agent incentives

Economic mechanisms administer the allocation of resources to interested agents based on their self-reported types. One objective in mechanism design is to design a strategyproof process so that no agent will have an incentive to misreport its type. However, typical analyses of the incentives properties of mechanisms operate under strong, usually untestable assumptions. Empirical, data-oriented approaches are, at best, under-developed. Furthermore, mechanism/policy evaluation methods usually ignore the dynamic nature of a multi-agent system and are thus inappropriate for estimating long-term effects. We introduce the problem of estimating the causal effects of mechanisms on incentives and frame it under the Rubin causal framework \citep{rubin74, rubin78}. This raises unique technical challenges since the outcome of interest (agent truthfulness) is confounded with strategic interactions and, interestingly, is typically never observed under any mechanism. We develop a methodology to estimate such causal effects that using a prior that is based on a strategic equilibrium model. Working on the domain of kidney exchanges, we show how to apply our methodology to estimate causal effects of kidney allocation mechanisms on hospitals' incentives. Our results demonstrate that the use of game-theoretic prior captures the dynamic nature of the kidney exchange multiagent system and shrinks the estimates towards long-term effects, thus improving upon typical methods that completely ignore agents' strategic behavior.

cs.GT↗

arXiv2009

FaceBots: Steps Towards Enhanced Long-Term Human-Robot Interaction by Utilizing and Publishing Online Social Information

Our project aims at supporting the creation of sustainable and meaningful longer-term human-robot relationships through the creation of embodied robots with face recognition and natural language dialogue capabilities, which exploit and publish social information available on the web (Facebook). Our main underlying experimental hypothesis is that such relationships can be significantly enhanced if the human and the robot are gradually creating a pool of shared episodic memories that they can co-refer to (shared memories), and if they are both embedded in a social web of other humans and robots they both know and encounter (shared friends). In this paper, we are presenting such a robot, which as we will see achieves two significant novelties.

cs.RO↗