arXiv subjects

Eric Bax

Publications and source records attributed to Eric Bax.

At least 19 recordsLinked to original sources

arXiv2024

Key Compression Limits for $k$-Minimum Value Sketches

The $k$-Minimum Values (\kmv) data sketch algorithm stores the $k$ least hash keys generated by hashing the items in a dataset. We show that compression based on ordering the keys and encoding successive differences can offer $O(\log n)$ bits per key in expected storage savings, where $n$ is the number of unique values in the data set. We also show that $O(\log n)$ expected bits saved per key is optimal for any form of compression for the $k$ least of $n$ random values -- that the encoding method is near-optimal among all methods to encode a \kmv sketch. We present a practical method to perform that compression, show that it is computationally efficient, and demonstrate that its average savings in practice is within about five percent of the theoretical minimum based on entropy. We verify that our method outperforms off-the-shelf compression methods, and we demonstrate that it is practical, using real and synthetic data.

cs.DS↗

arXiv2024

Steady Continuous Monitoring is (Just Barely) Impossible for Tests of Unbounded Length

AB testing evaluates the difference between a control and a treatment in a statistically rigorous manner. Continuous monitoring allows statistical evaluation of an AB test as it proceeds. One goal of continuous monitoring is early stopping -- confirming a statistically significant difference between control and treatment as soon as possible. Another goal is to maintain some statistical capability to discover significant differences later in the test if they cannot be confirmed earlier. These goals are in conflict -- looser requirements for early stopping leave us with more stringent ones for later. This paper shows that it is impossible to maintain a constant requirement for significance for tests that have no a priori stopping time, but we can come arbitrarily close to that goal by using tests that require repeated significant results to con rm statistically significant differences between treatment and control.

stat.ME↗

arXiv2024

Early Stopping Based on Repeated Significance

For a bucket test with a single criterion for success and a fixed number of samples or testing period, requiring a $p$-value less than a specified value of $\alpha$ for the success criterion produces statistical confidence at level $1 - \alpha$. For multiple criteria, a Bonferroni correction that partitions $\alpha$ among the criteria produces statistical confidence, at the cost of requiring lower $p$-values for each criterion. The same concept can be applied to decisions about early stopping, but that can lead to strict requirements for $p$-values. We show how to address that challenge by requiring criteria to be successful at multiple decision points.

stat.ME↗

arXiv2024

Pre- and Post-Auction Discounts in First-Price Auctions

One method to offer some bidders a discount in a first-price auction is to augment their bids when selecting a winner but only charge them their original bids should they win. Another method is to use their original bids to select a winner, then charge them a discounted price that is lower than their bid should they win. We show that the two methods have equivalent auction outcomes, for equal additive discounts and for multiplicative ones with appropriate adjustments to discount amounts. As a result, they have corresponding equilibria when equilibria exist. We also show that with the same level of multiplicative adjustments, bidders with discounts should prefer an augmented bid to a discounted price. Then we estimate optimal bid functions for valuation distributions based on data from online advertising auctions, and show how different discount levels affect auction outcomes for those bid functions.

cs.GT↗

arXiv2023

Matching Noisy Keys for Obfuscation

Data sketching has emerged as a key infrastructure for large-scale data analysis on streaming and distributed data. Merging sketches enables efficient estimation of cardinalities and frequency histograms over distributed data. However, merging sketches can require that each sketch stores hash codes for identifiers in different data sets or partitions, in order to perform effective matching. This can reveal identifiers during merging or across different data set or partition owners. This paper presents a framework to use noisy hash codes, with the noise level selected to obfuscate identifiers while allowing matching, with high probability. We give probabilistic error bounds on simultaneous obfuscation and matching, concluding that this is a viable approach.

cs.DS↗

arXiv2023

Non-asymptotic approximations for Pearson's chi-square statistic and its application to confidence intervals for strictly convex functions of the probability weights of discrete distributions

In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the multivariate normals with the same means and covariances. From the total variation bounds, we also derive a comparison of the cumulative distribution functions and quantile coupling inequalities between Pearson's chi-square statistic (written as the normalized quadratic form of a multinomial vector) and its multivariate normal analogue. We apply our results to find confidence intervals for the negative entropy of discrete distributions. Our method can be applied more generally to find confidence intervals for strictly convex functions of the weights of discrete distributions.

math.ST↗

arXiv2022

Sharp Frequency Bounds for Sample-Based Queries

A data sketch algorithm scans a big data set, collecting a small amount of data -- the sketch, which can be used to statistically infer properties of the big data set. Some data sketch algorithms take a fixed-size random sample of a big data set, and use that sample to infer frequencies of items that meet various criteria in the big data set. This paper shows how to statistically infer probably approximately correct (PAC) bounds for those frequencies, efficiently, and precisely enough that the frequency bounds are either sharp or off by only one, which is the best possible result without exact computation.

cs.LG↗

arXiv2021

Bounding Means of Discrete Distributions

We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with known category-based values. For small sample sizes, we show how to leverage the knowledge of the set of possible values to compute bounds that are stronger than for general random variables such as standard concentration inequalities.

math.ST↗

arXiv2021

Selecting a number of voters for a voting ensemble

For a voting ensemble that selects an odd-sized subset of the ensemble classifiers at random for each example, applies them to the example, and returns the majority vote, we show that any number of voters may minimize the error rate over an out-of-sample distribution. The optimal number of voters depends on the out-of-sample distribution of the number of classifiers in error. To select a number of voters to use, estimating that distribution then inferring error rates for numbers of voters gives lower-variance estimates than directly estimating those error rates.

cs.LG↗

arXiv2020

Heavy Tails Make Happy Buyers

In a second-price auction with i.i.d. (independent identically distributed) bidder valuations, adding bidders increases expected buyer surplus if the distribution of valuations has a sufficiently heavy right tail. While this does not imply that a bidder in an auction should prefer for more bidders to join the auction, it does imply that a bidder should prefer it in exchange for the bidder being allowed to participate in more auctions. Also, for a heavy-tailed valuation distribution, marginal expected seller revenue per added bidder remains strong even when there are already many bidders.

cs.GT↗

arXiv2019

Collecting Charges for Ad Impact on User Experience for Different Price Types

This note describes how to collect charges for ad impact on user experience. The charge may be per-view, to account for impact on user experience from viewing an ad, or per-click, to account for impact from clicking on the ad. The results for per-click charges also apply to per-conversion charges or per-action charges. Conceivably, a marketplace could assess both kinds of charges.

cs.GT↗

arXiv2019

Data Consortia

Today, web-based companies use user data to provide and enhance services to users, both individually and collectively. Some also analyze user data for other purposes, for example to select advertisements or price offers for users. Some even use or allow the data to be used to evaluate investments in financial markets. Users' concerns about how their data is or may be used has prompted legislative action in the European Union and congressional questioning in the United States. But data can also benefit society, for example giving early warnings for disease outbreaks, allowing in-depth study of relationships between genetics and disease, and elucidating local and macroeconomic trends in a timely manner. So, instead of just a focus on privacy, in the future, users may insist that their data be used on their behalf. We explore potential frameworks for groups of consenting, informed users to pool their data for their own benefit and that of society, discussing directions, challenges, and evolution for such efforts.

cs.CY↗

arXiv2019

Computing a Data Dividend

Quality data is a fundamental contributor to success in statistics and machine learning. If a statistical assessment or machine learning leads to decisions that create value, data contributors may want a share of that value. This paper presents methods to assess the value of individual data samples, and of sets of samples, to apportion value among different data contributors. We use Shapley values for individual samples and Owen values for combined samples, and show that these values can be computed in polynomial time in spite of their definitions having numbers of terms that are exponential in the number of samples.

cs.GT↗

arXiv2017

iPhone's Digital Marketplace: Characterizing the Big Spenders

With mobile shopping surging in popularity, people are spending ever more money on digital purchases through their mobile devices and phones. However, few large-scale studies of mobile shopping exist. In this paper we analyze a large data set consisting of more than 776M digital purchases made on Apple mobile devices that include songs, apps, and in-app purchases. We find that 61% of all the spending is on in-app purchases and that the top 1% of users are responsible for 59% of all the spending. These big spenders are more likely to be male and older, and less likely to be from the US. We study how they adopt and abandon individual app, and find that, after an initial phase of increased daily spending, users gradually lose interest: the delay between their purchases increases and the spending decreases with a sharp drop toward the end. Finally, we model the in-app purchasing behavior in multiple steps: 1) we model the time between purchases; 2) we train a classifier to predict whether the user will make a purchase from a new app or continue purchasing from the existing app; and 3) based on the outcome of the previous step, we attempt to predict the exact app, new or existing, from which the next purchase will come. The results yield new insights into spending habits in the mobile digital marketplace.

cs.SI↗

arXiv2016

Ensemble Validation: Selectivity has a Price, but Variety is Free

Suppose some classifiers are selected from a set of hypothesis classifiers to form an equally-weighted ensemble that selects a member classifier at random for each input example. Then the ensemble has an error bound consisting of the average error bound for the member classifiers, a term for selectivity that varies from zero (if all hypothesis classifiers are selected) to a standard uniform error bound (if only a single classifier is selected), and small constants. There is no penalty for using a richer hypothesis set if the same fraction of the hypothesis classifiers are selected for the ensemble.

stat.ML↗

arXiv2015

Some Theory For Practical Classifier Validation

We compare and contrast two approaches to validating a trained classifier while using all in-sample data for training. One is simultaneous validation over an organized set of hypotheses (SVOOSH), the well-known method that began with VC theory. The other is withhold and gap (WAG). WAG withholds a validation set, trains a holdout classifier on the remaining data, uses the validation data to validate that classifier, then adds the rate of disagreement between the holdout classifier and one trained using all in-sample data, which is an upper bound on the difference in error rates. We show that complex hypothesis classes and limited training data can make WAG a favorable alternative.

stat.ML↗

arXiv2015

Exponential Weight Functions for Quasi-Proportional Auctions

In quasi-proportional auctions, the allocation is shared among bidders in proportion to their weighted bids. The auctioneer selects a bid weight function, and bidders know the weight function when they bid. In this note, we analyze how weight functions that are exponential in the bid affect bidder behavior. We show that exponential weight functions have a pure-strategy Nash equilibrium, we characterize bids at an equilibrium, and we compare it to an equilibrium for power weight functions.

cs.GT↗

arXiv2015

VCG Payments for Portfolio Allocations in Online Advertising

Some online advertising offers pay only when an ad elicits a response. Randomness and uncertainty about response rates make showing those ads a risky investment for online publishers. Like financial investors, publishers can use portfolio allocation over multiple advertising offers to pursue revenue while controlling risk. Allocations over multiple offers do not have a distinct winner and runner-up, so the usual second-price mechanism does not apply. This paper develops a pricing mechanism for portfolio allocations. The mechanism is efficient, truthful, and rewards offers that reduce risk.

cs.GT↗