arXiv subjects

David Jensen

Publications and source records attributed to David Jensen.

At least 55 records · Page 3Linked to original sources

arXiv2021

Preserving Privacy in Personalized Models for Distributed Mobile Services

The ubiquity of mobile devices has led to the proliferation of mobile services that provide personalized and context-aware content to their users. Modern mobile services are distributed between end-devices, such as smartphones, and remote servers that reside in the cloud. Such services thrive on their ability to predict future contexts to pre-fetch content or make context-specific recommendations. An increasingly common method to predict future contexts, such as location, is via machine learning (ML) models. Recent work in context prediction has focused on ML model personalization where a personalized model is learned for each individual user in order to tailor predictions or recommendations to a user's mobile behavior. While the use of personalized models increases efficacy of the mobile service, we argue that it increases privacy risk since a personalized model encodes contextual behavior unique to each user. To demonstrate these privacy risks, we present several attribute inference-based privacy attacks and show that such attacks can leak privacy with up to 78% efficacy for top-3 predictions. We present Pelican, a privacy-preserving personalization system for context-aware mobile services that leverages both device and cloud resources to personalize ML models while minimizing the risk of privacy leakage for users. We evaluate Pelican using real world traces for location-aware mobile services and show that Pelican can substantially reduce privacy leakage by up to 75%.

cs.DC↗

arXiv2020

Brill-Noether theory for curves of a fixed gonality

We prove a generalization of the Brill-Noether theorem for the variety of special divisors $W^r_d(C)$ on a general curve $C$ of prescribed gonality. Our main theorem gives a closed formula for the dimension of $W^r_d(C)$. We build on previous work of Pflueger, who used an analysis of the tropical divisor theory of special chains of cycles to give upper bounds on the dimensions of Brill--Noether varieties on such curves. We prove his conjecture, that this upper bound is achieved for a general curve. Our methods introduce logarithmic stable maps as a systematic tool in Brill-Noether theory. A precise relation between the divisor theory on chains of cycles and the corresponding tropical maps theory is exploited to prove new regeneration theorems for linear series with negative Brill-Noether number. The strategy involves blending an analysis of obstruction theories for logarithmic stable maps with the geometry of Berkovich curves. To show the utility of these methods, we provide a short new derivation of lifting for special divisors on a chain of cycles with generic edge lengths, proved using different techniques by Cartwright, Jensen, and Payne. A crucial technical result is a new realizability theorem for tropical stable maps in obstructed geometries, generalizing a well-known theorem of Speyer on genus one curves to arbitrary genus.

math.AG↗

arXiv2020

Tropical Methods in Hurwitz-Brill-Noether Theory

Splitting type loci are the natural generalizations of Brill-Noether varieties for curves with a distinguished map to the projective line. We give a tropical proof of a theorem of H. Larson, showing that splitting type loci have the expected dimension for general elements of the Hurwitz space. Our proof uses an explicit description of splitting type loci on a certain family of tropical curves. We further show that these tropical splitting type loci are connected in codimension one, and describe an algorithm for computing their cardinality when they are zero-dimensional. We provide a conjecture for the numerical class of splitting type loci, which we confirm in a number of cases.

math.AG↗

arXiv2020

Causal Inference using Gaussian Processes with Structured Latent Confounders

Latent confounders---unobserved variables that influence both treatment and outcome---can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by the course's difficulty in addition to any educational interventions they receive individually. This paper shows how to semiparametrically model latent confounders that have this structure and thereby improve estimates of causal effects. The key innovations are a hierarchical Bayesian model, Gaussian processes with structured latent confounders (GP-SLC), and a Monte Carlo inference algorithm for this model based on elliptical slice sampling. GP-SLC provides principled Bayesian uncertainty estimates of individual treatment effect with minimal assumptions about the functional forms relating confounders, covariates, treatment, and outcome. Finally, this paper shows GP-SLC is competitive with or more accurate than widely used causal inference techniques on three benchmark datasets, including the Infant Health and Development Program and a dataset showing the effect of changing temperatures on state-wide energy consumption across New England.

stat.ME↗

arXiv2020

Text and Causal Inference: A Review of Using Text to Remove Confounding from Causal Estimates

Many applications of computational social science aim to infer causal conclusions from non-experimental data. Such observational data often contains confounders, variables that influence both potential causes and potential effects. Unmeasured or latent confounders can bias causal estimates, and this has motivated interest in measuring potential confounders from observed text. For example, an individual's entire history of social media posts or the content of a news article could provide a rich measurement of multiple confounders. Yet, methods and applications for this problem are scattered across different communities and evaluation practices are inconsistent. This review is the first to gather and categorize these examples and provide a guide to data-processing and evaluation decisions. Despite increased attention on adjusting for confounding using text, there are still many open problems, which we highlight in this paper.

cs.CL↗

arXiv2020

Exploratory Not Explanatory: Counterfactual Analysis of Saliency Maps for Deep Reinforcement Learning

Saliency maps are frequently used to support explanations of the behavior of deep reinforcement learning (RL) agents. However, a review of how saliency maps are used in practice indicates that the derived explanations are often unfalsifiable and can be highly subjective. We introduce an empirical approach grounded in counterfactual reasoning to test the hypotheses generated from saliency maps and assess the degree to which they correspond to the semantics of RL environments. We use Atari games, a common benchmark for deep RL, to evaluate three types of saliency maps. Our results show the extent to which existing claims about Atari games can be evaluated and suggest that saliency maps are best viewed as an exploratory tool rather than an explanatory tool.

cs.LG↗

arXiv2019

The Case for Evaluating Causal Models Using Interventional Measures and Empirical Data

Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances algorithms that learn causal models from data, and this work has produced a series of impressive technical advances. However, evaluation techniques for causal modeling algorithms have remained somewhat primitive, limiting what we can learn from experimental studies of algorithm performance, constraining the types of algorithms and model representations that researchers consider, and creating a gap between theory and practice. We argue for more frequent use of evaluation techniques that examine interventional measures rather than structural or observational measures, and that evaluate those measures on empirical data rather than synthetic data. We survey the current practice in evaluation and show that the techniques we recommend are rarely used in practice. We show that such techniques are feasible and that data sets are available to conduct such evaluations. We also show that these techniques produce substantially different results than using structural measures and synthetic data.

cs.AI↗

arXiv2019

Bayesian causal inference via probabilistic program synthesis

Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach using a sufficiently expressive probabilistic programming language. Priors are represented using probabilistic programs that generate source code in a domain specific language. Interventions are represented using probabilistic programs that edit this source code to modify the original generative process. This approach makes it straightforward to incorporate data from atomic interventions, as well as shift interventions, variance-scaling interventions, and other interventions that modify causal structure. This approach also enables the use of general-purpose inference machinery for probabilistic programs to infer probable causal structures and parameters from data. This abstract describes a prototype of this approach in the Gen probabilistic programming language.

cs.AI↗

arXiv2019

The motivic zeta functions of a matroid

We introduce motivic zeta functions for matroids. These zeta functions are defined as sums over the lattice points of Bergman fans, and in the realizable case, they coincide with the motivic Igusa zeta functions of hyperplane arrangements. We show that these motivic zeta functions satisfy a functional equation arising from matroid Poincaré duality in the sense of Adiprasito-Huh-Katz. In the process, we obtain a formula for the Hilbert series of the cohomology ring of a matroid, in the sense of Feichtner-Yuzvinsky. We then show that our motivic zeta functions specialize to the topological zeta functions for matroids introduced by van der Veer, and we compute the first two coefficients in the Taylor expansion of these topological zeta functions, providing affirmative answers to two questions posed by van der Veer.

math.CO↗

arXiv2019

Components of Brill-Noether Loci for Curves with Fixed Gonality

We describe a conjectural stratification of the Brill-Noether variety for general curves of fixed genus and gonality. As evidence for this conjecture, we show that this Brill-Noether variety has at least as many irreducible components as predicted by the conjecture, and that each of these components has the expected dimension. Our proof uses combinatorial and tropical techniques. Specifically, we analyze containment relations between the various strata of tropical Brill-Noether loci identified by Pflueger in his classification of special divisors on chains of loops.

math.AG↗

arXiv2019

Toybox: A Suite of Environments for Experimental Evaluation of Deep Reinforcement Learning

Evaluation of deep reinforcement learning (RL) is inherently challenging. In particular, learned policies are largely opaque, and hypotheses about the behavior of deep RL agents are difficult to test in black-box environments. Considerable effort has gone into addressing opacity, but almost no effort has been devoted to producing high quality environments for experimental evaluation of agent behavior. We present TOYBOX, a new high-performance, open-source* subset of Atari environments re-designed for the experimental evaluation of deep RL. We show that TOYBOX enables a wide range of experiments and analyses that are impossible in other environments. *https://kdl-umass.github.io/Toybox/

cs.LG↗

arXiv2019

Let's Play Again: Variability of Deep Reinforcement Learning Agents in Atari Environments

Reproducibility in reinforcement learning is challenging: uncontrolled stochasticity from many sources, such as the learning algorithm, the learned policy, and the environment itself have led researchers to report the performance of learned agents using aggregate metrics of performance over multiple random seeds for a single environment. Unfortunately, there are still pernicious sources of variability in reinforcement learning agents that make reporting common summary statistics an unsound metric for performance. Our experiments demonstrate the variability of common agents used in the popular OpenAI Baselines repository. We make the case for reporting post-training agent performance as a distribution, rather than a point estimate.

cs.LG↗

arXiv2019

ToyBox: Better Atari Environments for Testing Reinforcement Learning Agents

It is a widely accepted principle that software without tests has bugs. Testing reinforcement learning agents is especially difficult because of the stochastic nature of both agents and environments, the complexity of state-of-the-art models, and the sequential nature of their predictions. Recently, the Arcade Learning Environment (ALE) has become one of the most widely used benchmark suites for deep learning research, and state-of-the-art Reinforcement Learning (RL) agents have been shown to routinely equal or exceed human performance on many ALE tasks. Since ALE is based on emulation of original Atari games, the environment does not provide semantically meaningful representations of internal game state. This means that ALE has limited utility as an environment for supporting testing or model introspection. We propose ToyBox, a collection of reimplementations of these games that solves this critical problem and enables robust testing of RL agents.

cs.AI↗

arXiv2018

Measuring and Characterizing Generalization in Deep Reinforcement Learning

Deep reinforcement-learning methods have achieved remarkable performance on challenging control tasks. Observations of the resulting behavior give the impression that the agent has constructed a generalized representation that supports insightful action decisions. We re-examine what is meant by generalization in RL, and propose several definitions based on an agent's performance in on-policy, off-policy, and unreachable states. We propose a set of practical methods for evaluating agents with these definitions of generalization. We demonstrate these techniques on a common benchmark task for deep RL, and we show that the learned networks make poor decisions for states that differ only slightly from on-policy states, even though those states are not selected adversarially. Taken together, these results call into question the extent to which deep Q-networks learn generalized representations, and suggest that more experimentation and analysis is necessary before claims of representation learning can be supported.

cs.LG↗

arXiv2018

On the strong maximal rank conjecture in genus 22 and 23

We develop new methods to study tropicalizations of linear series and show linear independence of sections. Using these methods, we prove two new cases of the strong maximal rank conjecture for linear series of degree 25 and 26 on curves of genus 22 and 23, respectively.

math.AG↗

arXiv2018

Tropicalization of theta characteristics, double covers, and Prym varieties

We study the behavior of theta characteristics on an algebraic curve under the specialization map to a tropical curve. We show that each effective theta characteristic on the tropical curve is the specialization of $2^{g-1}$ even theta characteristics and $2^{g-1}$ odd theta characteristics. We then study the relationship between unramified double covers of a tropical curve and its theta characteristics, and use this to define the tropical Prym variety.

math.AG↗

arXiv2017

Brill-Noether theory of curves on $\mathbb{P}^1 \times \mathbb{P}^1$: tropical and classical approach

The gonality sequence $(d_r)_{r\geq1}$ of a smooth algebraic curve comprises the minimal degrees $d_r$ of linear systems of rank $r$. We explain two approaches to compute the gonality sequence of smooth curves in $\mathbb{P}^1 \times \mathbb{P}^1$: a tropical and a classical approach. The tropical approach uses the recently developed Brill--Noether theory on tropical curves and Baker's specialization of linear systems from curves to metric graphs. The classical one extends the work of Hartshorne on plane curves to curves on $\mathbb{P}^1 \times \mathbb{P}^1$.

math.AG↗

arXiv2017

Realization of groups with pairing as Jacobians of finite graphs

We study which groups with pairing can occur as the Jacobian of a finite graph. We provide explicit constructions of graphs whose Jacobian realizes a large fraction of odd groups with a given pairing. Conditional on the generalized Riemann hypothesis, these constructions yield all groups with pairing of odd order, and unconditionally, they yield all groups with pairing whose prime factors are sufficiently large. For groups with pairing of even order, we provide a partial answer to this question, for a certain restricted class of pairings. Finally, we explore which finite abelian groups occur as the Jacobian of a simple graph. There exist infinite families of finite abelian groups that do not occur as the Jacobians of simple graphs.

math.CO↗