Personalized Dynamic Pricing with Machine Learning: High-Dimensional Features and Heterogeneous Elasticity

2021 ◽  
Author(s):  
Gah-Yi Ban ◽  
N. Bora Keskin
Keyword(s):  
Dynamic Pricing ◽  
Simulated Data ◽  
The United States ◽  
Model Parameters ◽  
Data Sets ◽  
Demand Model ◽  
Pricing Policy ◽  
Data Set ◽  
Customized Pricing ◽  
The Individual

We consider a seller who can dynamically adjust the price of a product at the individual customer level, by utilizing information about customers’ characteristics encoded as a d-dimensional feature vector. We assume a personalized demand model, parameters of which depend on s out of the d features. The seller initially does not know the relationship between the customer features and the product demand but learns this through sales observations over a selling horizon of T periods. We prove that the seller’s expected regret, that is, the revenue loss against a clairvoyant who knows the underlying demand relationship, is at least of order [Formula: see text] under any admissible policy. We then design a near-optimal pricing policy for a semiclairvoyant seller (who knows which s of the d features are in the demand model) who achieves an expected regret of order [Formula: see text]. We extend this policy to a more realistic setting, where the seller does not know the true demand predictors, and show that this policy has an expected regret of order [Formula: see text], which is also near-optimal. Finally, we test our theory on simulated data and on a data set from an online auto loan company in the United States. On both data sets, our experimentation-based pricing policy is superior to intuitive and/or widely-practiced customized pricing methods, such as myopic pricing and segment-then-optimize policies. Furthermore, our policy improves upon the loan company’s historical pricing decisions by 47% in expected revenue over a six-month period. This paper was accepted by Noah Gans, stochastic models and simulation.

scholarly journals Model-Based Geostatistics from a Bayesian Perspective: Investigating Area-to-Point Kriging with Small Data Sets

2019 ◽  
Vol 52 (3) ◽  
pp. 397-423
Author(s):  
Luc Steinbuch ◽  
Thomas G. Orton ◽  
Dick J. Brus
Keyword(s):  
Prior Distribution ◽  
Crop Yields ◽  
Simulated Data ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Small Data ◽  
Data Sets ◽  
Data Set ◽  
Minimal Impact ◽  
The Impact

AbstractArea-to-point kriging (ATPK) is a geostatistical method for creating high-resolution raster maps using data of the variable of interest with a much lower resolution. The data set of areal means is often considerably smaller ($$<\,50 $$<50 observations) than data sets conventionally dealt with in geostatistical analyses. In contemporary ATPK methods, uncertainty in the variogram parameters is not accounted for in the prediction; this issue can be overcome by applying ATPK in a Bayesian framework. Commonly in Bayesian statistics, posterior distributions of model parameters and posterior predictive distributions are approximated by Markov chain Monte Carlo sampling from the posterior, which can be computationally expensive. Therefore, a partly analytical solution is implemented in this paper, in order to (i) explore the impact of the prior distribution on predictions and prediction variances, (ii) investigate whether certain aspects of uncertainty can be disregarded, simplifying the necessary computations, and (iii) test the impact of various model misspecifications. Several approaches using simulated data, aggregated real-world point data, and a case study on aggregated crop yields in Burkina Faso are compared. The prior distribution is found to have minimal impact on the disaggregated predictions. In most cases with known short-range behaviour, an approach that disregards uncertainty in the variogram distance parameter gives a reasonable assessment of prediction uncertainty. However, some severe effects of model misspecification in terms of overly conservative or optimistic prediction uncertainties are found, highlighting the importance of model choice or integration into ATPK.

scholarly journals Dynamic Learning and Pricing with Model Misspecification

2019 ◽  
Vol 65 (11) ◽  
pp. 4980-5000 ◽  
Author(s):  
Mila Nambiar ◽  
David Simchi-Levi ◽  
He Wang
Keyword(s):  
Price Elasticity ◽  
Operations Management ◽  
Dynamic Pricing ◽  
Contextual Information ◽  
Model Misspecification ◽  
Model Parameters ◽  
Demand Model ◽  
Dynamic Learning ◽  
Data Set ◽  
Performance Guarantees

We study a multiperiod dynamic pricing problem with contextual information, where the seller uses a misspecified demand model. The seller sequentially observes past demand, updates model parameters, and then chooses the price for the next period based on time-varying features. We show that model misspecification leads to a correlation between price and prediction error of demand per period, which, in turn, leads to inconsistent price elasticity estimates and hence suboptimal pricing decisions. We propose a “random price shock” (RPS) algorithm that dynamically generates randomized price shocks to estimate price elasticity, while maximizing revenue. We show that the RPS algorithm has strong theoretical performance guarantees, that it is robust to model misspecification, and that it can be adapted to a number of business settings, including (1) when the feasible price set is a price ladder and (2) when the contextual information is not IID. We also perform offline simulations to gauge the performance of RPS on a large fashion retail data set and find that is expected to earn 8%–20% more revenue on average than competing algorithms that do not account for price endogeneity. This paper was accepted by Serguei Netessine, operations management.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

Origins and Destinations – Social Security Claimant Dynamics

1998 ◽  
Vol 27 (3) ◽  
pp. 351-369 ◽  
Author(s):  
MICHAEL NOBLE ◽  
SIN YI CHEUNG ◽  
GEORGE SMITH
Keyword(s):  
The United States ◽  
Data Sets ◽  
Income Support ◽  
Data Set ◽  
Family Structures ◽  
Highly Educated ◽  
Lone Parents ◽  
Lone Mothers ◽  
Time Period ◽  
Short Time

This article briefly reviews American and British literature on welfare dynamics and examines the concepts of welfare dependency and ‘dependency culture’ with particular reference to lone parents. Using UK benefit data sets, the welfare dynamics of lone mothers are examined to explore the extent to which they inform the debates. Evidence from Housing Benefits data show that even over a relatively short time period, there is significant turnover in the benefits-dependent lone parent population with movement in and out of income support as well as movement into other family structures. Younger lone parents and owner-occupiers tend to leave the data set while older lone parents and council tenants are most likely to stay. Some owner-occupier lone parents may be relatively well off and on income support for a relatively short time between separation and a financial settlement being reached. They may also represent a more highly educated and highly skilled group with easier access to the labour market than renters. Any policy moves paralleling those in the United States to time limit benefit will disproportionately affect older lone parents.

scholarly journals Variational inference using approximate likelihood under the coalescent with recombination

2021 ◽  
pp. gr.273631.120
Author(s):  
Xinhao Liu ◽  
Huw A Ogilvie ◽  
Luay Nakhleh
Keyword(s):  
Simulated Data ◽  
Variational Inference ◽  
Divide And Conquer ◽  
Data Sets ◽  
Transition Rates ◽  
Data Set ◽  
Population Sizes ◽  
Novel Method ◽  
Approximate Likelihood ◽  
Promising Avenue

Coalescent methods are proven and powerful tools for population genetics, phylogenetics, epidemiology, and other fields. A promising avenue for the analysis of large genomic alignments, which are increasingly common, are coalescent hidden Markov model (coalHMM) methods, but these methods have lacked general usability and flexibility. We introduce a novel method for automatically learning a coalHMM and inferring the posterior distributions of evolutionary parameters using black-box variational inference, with the transition rates between local genealogies derived empirically by simulation. This derivation enables our method to work directly with three or four taxa and through a divide-and-conquer approach with more taxa. Using a simulated data set resembling a human-chimp-gorilla scenario, we show that our method has comparable or better accuracy to previous coalHMM methods. Both species divergence times and population sizes were accurately inferred. The method also infers local genealogies and we report on their accuracy. Furthermore, we discuss a potential direction for scaling the method to larger data sets through a divide-and-conquer approach. This accuracy means our method is useful now, and by deriving transition rates by simulation it is flexible enough to enable future implementations of all kinds of population models.

scholarly journals Efficient detection of repeating sites to accelerate phylogenetic likelihood calculations

2016 ◽  
Author(s):  
Kassian Kobert ◽  
Alexandros Stamatakis ◽  
Tomáš Flouri
Keyword(s):  
Evolutionary Biology ◽  
Likelihood Function ◽  
Simulated Data ◽  
Evolutionary Model ◽  
Identical Result ◽  
Model Parameters ◽  
Data Sets ◽  
Efficient Detection ◽  
Novel Method ◽  
Computational Bottleneck

The phylogenetic likelihood function is the major computational bottleneck in several applications of evolutionary biology such as phylogenetic inference, species delimitation, model selection and divergence times estimation. Given the alignment, a tree and the evolutionary model parameters, the likelihood function computes the conditional likelihood vectors for every node of the tree. Vector entries for which all input data are identical result in redundant likelihood operations which, in turn, yield identical conditional values. Such operations can be omitted for improving run-time and, using appropriate data structures, reducing memory usage. We present a fast, novel method for identifying and omitting such redundant operations in phylogenetic likelihood calculations, and assess the performance improvement and memory saving attained by our method. Using empirical and simulated data sets, we show that a prototype implementation of our method yields up to 10-fold speedups and uses up to 78% less memory than one of the fastest and most highly tuned implementations of the phylogenetic likelihood function currently available. Our method is generic and can seamlessly be integrated into any phylogenetic likelihood implementation.

scholarly journals The GTC exoplanet transit spectroscopy survey

2019 ◽  
Vol 622 ◽  
pp. A172 ◽  
Author(s):  
F. Murgas ◽  
G. Chen ◽  
E. Pallé ◽  
L. Nortmann ◽  
G. Nowak
Keyword(s):  
Transmission Spectrum ◽  
Rayleigh Scattering ◽  
Extrasolar Planets ◽  
Light Curves ◽  
Data Sets ◽  
Transmission Spectra ◽  
Data Set ◽  
Systematic Effects ◽  
The Individual ◽  
Spectrum Slope

Context. Rayleigh scattering in a hydrogen-dominated exoplanet atmosphere can be detected using ground- or space-based telescopes. However, stellar activity in the form of spots can mimic Rayleigh scattering in the observed transmission spectrum. Quantifying this phenomena is key to our correct interpretation of exoplanet atmospheric properties. Aims. We use the ten-meter Gran Telescopio Canarias (GTC) telescope to carry out a ground-based transmission spectra survey of extrasolar planets to characterize their atmospheres. In this paper we investigate the exoplanet HAT-P-11b, a Neptune-sized planet orbiting an active K-type star. Methods. We obtained long-slit optical spectroscopy of two transits of HAT-P-11b with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) on August 30, 2016 and September 25, 2017. We integrated the spectrum of HAT-P-11 and one reference star in several spectroscopic channels across the λ ~ 400–785 nm region, creating numerous light curves of the transits. We fit analytic transit curves to the data taking into account the systematic effects and red noise present in the time series in an effort to measure the change of the planet-to-star radius ratio (Rp∕Rs) across wavelength. Results. By fitting both transits together, we find a slope in the transmission spectrum showing an increase of the planetary radius towards blue wavelengths. Closer inspection of the transmission spectrum of the individual data sets reveals that the first transit presents this slope while the transmission spectrum of the second data set is flat. Additionally, we detect hints of Na absorption on the first night, but not on the second. We conclude that the transmission spectrum slope and Na absorption excess found in the first transit observation are caused by unocculted stellar spots. Modeling the contribution of unocculted spots to reproduce the results of the first night we find a spot filling factor of δ = 0.62−0.17+0.20 and a spot-to-photosphere temperature difference of ΔT = 429−299+184 K.

scholarly journals Bayesian Planet Searches for the 10 cm/s Radial Velocity Era

2015 ◽  
Vol 11 (A29A) ◽  
pp. 205-207
Author(s):  
Philip C. Gregory
Keyword(s):  
Radial Velocity ◽  
State Of The Art ◽  
Simulated Data ◽  
Model Parameters ◽  
Data Sets ◽  
Stellar Activity ◽  
Bayesian Fusion ◽  
Multiple State ◽  
Simulated Data Sets ◽  
Apodization Function

AbstractA new apodized Keplerian model is proposed for the analysis of precision radial velocity (RV) data to model both planetary and stellar activity (SA) induced RV signals. A symmetrical Gaussian apodization function with unknown width and center can distinguish planetary signals from SA signals on the basis of the width of the apodization function. The general model for m apodized Keplerian signals also includes a linear regression term between RV and the stellar activity diagnostic In (R'hk), as well as an extra Gaussian noise term with unknown standard deviation. The model parameters are explored using a Bayesian fusion MCMC code. A differential version of the Generalized Lomb-Scargle periodogram provides an additional way of distinguishing SA signals and helps guide the choice of new periods. Sample results are reported for a recent international RV blind challenge which included multiple state of the art simulated data sets supported by a variety of stellar activity diagnostics.

US academic libraries' staffing and expenditure trends (1996–2016)

2020 ◽  
Vol 41 (4/5) ◽  
pp. 247-268 ◽  
Author(s):  
Starr Hoffman ◽  
Samantha Godbey
Keyword(s):  
Academic Libraries ◽  
The United States ◽  
Data Sets ◽  
Size Category ◽  
Data Set ◽  
Content Type ◽  
Education Statistics ◽  
Trends Over Time ◽  
Doctoral Institutions ◽  
Over Time

PurposeThis paper explores trends over time in library staffing and staffing expenditures among two- and four-year colleges and universities in the United States.Design/methodology/approachResearchers merged and analyzed data from 1996 to 2016 from the National Center for Education Statistics for over 3,500 libraries at postsecondary institutions. This study is primarily descriptive in nature and addresses the research questions: How do staffing trends in academic libraries over this period of time relate to Carnegie classification and institution size? How do trends in library staffing expenditures over this period of time correspond to these same variables?FindingsAcross all institutions, on average, total library staff decreased from 1998 to 2012. Numbers of librarians declined at master’s and doctoral institutions between 1998 and 2016. Numbers of students per librarian increased over time in each Carnegie and size category. Average inflation-adjusted staffing expenditures have remained steady for master's, baccalaureate and associate's institutions. Salaries as a percent of library budget decreased only among doctoral institutions and institutions with 20,000 or more students.Originality/valueThis is a valuable study of trends over time, which has been difficult without downloading and merging separate data sets from multiple government sources. As a result, few studies have taken such an approach to this data. Consequently, institutions and libraries are making decisions about resource allocation based on only a fraction of the available data. Academic libraries can use this study and the resulting data set to benchmark key staffing characteristics.

A classification approach based on variable precision rough sets and cluster validity index function

2014 ◽  
Vol 31 (8) ◽  
pp. 1778-1789
Author(s):  
Hongkang Lin
Keyword(s):  
Optimal Number ◽  
Data Sets ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Index Method ◽  
Data Set ◽  
Content Type ◽  
The Individual ◽  
Variable Precision Rough Sets ◽  
Optimal Number Of Clusters

Purpose – The clustering/classification method proposed in this study, designated as the PFV-index method, provides the means to solve the following problems for a data set characterized by imprecision and uncertainty: first, discretizing the continuous values of all the individual attributes within a data set; second, evaluating the optimality of the discretization results; third, determining the optimal number of clusters per attribute; and fourth, improving the classification accuracy (CA) of data sets characterized by uncertainty. The paper aims to discuss these issues. Design/methodology/approach – The proposed method for the solution of the clustering/classifying problem, designated as PFV-index method, combines a particle swarm optimization algorithm, fuzzy C-means method, variable precision rough sets theory, and a new cluster validity index function. Findings – This method could cluster the values of the individual attributes within the data set and achieves both the optimal number of clusters and the optimal CA. Originality/value – The validity of the proposed approach is investigated by comparing the classification results obtained for UCI data sets with those obtained by supervised classification BPNN, decision-tree methods.

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