arXiv subjects

Jan Pedersen

Publications and source records attributed to Jan Pedersen.

11 recordsLinked to original sources

arXiv2025

Verifying Correctness of Shared Channels in a Cooperatively Scheduled Process-Oriented Language

Correct concurrent behaviour is important in understanding how components will act within certain conditions. In this work. we analyse the behaviour of shared communicating channels within a coorporatively scheduled runtime. We use the refinement checking and modelling tool FDR to develop both specifications of how such shared channels should behave and models of the implementations of these channels in the cooperatively scheduled language ProcessJ. Our results demonstrate that although we can certainly implement the correct behaviour of such channels, the outcome is dependant on having adequate resources available to execute all processes involved. We conclude that modelling the runtime environment of concurrent components is necessary to ensure components behave as specified in the real world.

cs.PL↗

arXiv2024

Long or Short or Both? An Exploration on Lookback Time Windows of Behavioral Features in Product Search Ranking

Customer shopping behavioral features are core to product search ranking models in eCommerce. In this paper, we investigate the effect of lookback time windows when aggregating these features at the (query, product) level over history. By studying the pros and cons of using long and short time windows, we propose a novel approach to integrating these historical behavioral features of different time windows. In particular, we address the criticality of using query-level vertical signals in ranking models to effectively aggregate all information from different behavioral features. Anecdotal evidence for the proposed approach is also provided using live product search traffic on Walmart.com.

cs.IR↗

arXiv2020

Heterogeneous Causal Learning for Effectiveness Optimization in User Marketing

User marketing is a key focus of consumer-based internet companies. Learning algorithms are effective to optimize marketing campaigns which increase user engagement, and facilitates cross-marketing to related products. By attracting users with rewards, marketing methods are effective to boost user activity in the desired products. Rewards incur significant cost that can be off-set by increase in future revenue. Most methodologies rely on churn predictions to prevent losing users to make marketing decisions, which cannot capture up-lift across counterfactual outcomes with business metrics. Other predictive models are capable of estimating heterogeneous treatment effects, but fail to capture the balance of cost versus benefit. We propose a treatment effect optimization methodology for user marketing. This algorithm learns from past experiments and utilizes novel optimization methods to optimize cost efficiency with respect to user selection. The method optimizes decisions using deep learning optimization models to treat and reward users, which is effective in producing cost-effective, impactful marketing campaigns. Our methodology demonstrates superior algorithmic flexibility with integration with deep learning methods and dealing with business constraints. The effectiveness of our model surpasses the quasi-oracle estimation (R-learner) model and causal forests. We also established evaluation metrics that reflect the cost-efficiency and real-world business value. Our proposed constrained and direct optimization algorithms outperform by 24.6% compared with the best performing method in prior art and baseline methods. The methodology is useful in many product scenarios such as optimal treatment allocation and it has been deployed in production world-wide.

cs.LG↗

arXiv2020

Learning Continuous Treatment Policy and Bipartite Embeddings for Matching with Heterogeneous Causal Effects

Causal inference methods are widely applied in the fields of medicine, policy, and economics. Central to these applications is the estimation of treatment effects to make decisions. Current methods make binary yes-or-no decisions based on the treatment effect of a single outcome dimension. These methods are unable to capture continuous space treatment policies with a measure of intensity. They also lack the capacity to consider the complexity of treatment such as matching candidate treatments with the subject. We propose to formulate the effectiveness of treatment as a parametrizable model, expanding to a multitude of treatment intensities and complexities through the continuous policy treatment function, and the likelihood of matching. Our proposal to decompose treatment effect functions into effectiveness factors presents a framework to model a rich space of actions using causal inference. We utilize deep learning to optimize the desired holistic metric space instead of predicting single-dimensional treatment counterfactual. This approach employs a population-wide effectiveness measure and significantly improves the overall effectiveness of the model. The performance of our algorithms is. demonstrated with experiments. When using generic continuous space treatments and matching architecture, we observe a 41% improvement upon prior art with cost-effectiveness and 68% improvement upon a similar method in the average treatment effect. The algorithms capture subtle variations in treatment space, structures the efficient optimizations techniques, and opens up the arena for many applications.

cs.LG↗

arXiv2018

Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages

The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such quantities in the case where the stationary process is a discretely sampled continuous-time moving average driven by a L\'{e}vy process. We obtain sufficient conditions, in terms of the kernel of the moving and the coefficients of the quadratic form, ensuring that the centered and adequately normalized version of the quadratic form converges weakly to a Gaussian limit.

math.PR↗

arXiv2018

Multivariate stochastic delay differential equations and CAR representations of CARMA processes

In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a continuous-time equivalent of the AR($\infty$) representation. Furthermore, we show how this representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.

math.PR↗

arXiv2017

On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos

Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient conditions. The case where both components consist of a sum of two Gaussian squares is treated in more depth, and it is conjectured that such vectors are infinitely divisible.

math.PR↗

arXiv2017

Equivalent martingale measures for L\'evy-driven moving averages and related processes

In the present paper we obtain sufficient conditions for the existence of equivalent martingale measures for L\'{e}vy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions, also necessary. For instance, this is the case for moving averages driven by an $\alpha$-stable L\'{e}vy process with $\alpha \in (1,2]$. Our proofs rely on various techniques for showing the martingale property of stochastic exponentials.

math.PR↗

arXiv2017

Continuous-time models with an autoregressive structure

In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general stochastic delay differential equations, will be given particular attention. We use the obtained results to link the introduced processes to both discrete-time and continuous-time ARMA processes.

math.PR↗

arXiv2012

On stochastic integration for volatility modulated L\'{e}vy-driven Volterra processes

This papers develops a stochastic integration theory with respect to volatility modulated L\'{e}vy-driven Volterra (VMLV) processes. It extends recent results in the literature to allow for stochastic volatility and pure jump processes in the integrator. The new integration operator is based on Malliavin calculus and describes an anticipative integral. Fundamental properties of the integral are derived and important applications are given.

math.PR↗

arXiv2010

Martingale-type processes indexed by the real line

Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to minus infinity in relation to the quadratic variation or the predictable quadratic variation, and we relate the limiting behavior to the martingale property. Finally, integration with respect to an increment martingale is studied.

math.PR↗