arXiv subjects

Mohamad Elmasri

Publications and source records attributed to Mohamad Elmasri.

10 recordsLinked to original sources

arXiv2026

Pricing rides as option contracts: guarantees and memberships under travel-time uncertainty

Modern ride-share platforms must commit to a price before a trip is taken, yet the realized fare depends on travel time that is uncertain at the moment of sale, which can occur days in advance. The upfront price thus decomposes into the expected fare and the premium on an insurance claim whose payoff is the shortfall between the realized and promised prices. This work computes the fair premium for such a claim, following from contingent-claim pricing. Recent advances in travel-time distribution modeling cast the asymptotic distribution of travel time as a Brownian motion on a metric graph carrying a cyclostationary travel-time process. We thus derive closed-form premiums under both a population and a route-conditional travel-time law. A single pricing equation then covers products of increasing informational difficulty, such as on-demand and scheduled rides and capped-membership and commuter products. To price on sparse data, we develop route and travel-time samplers and validate them out of sample on 2014 Quebec City GPS trips, where they reproduce the empirical trip-time distribution. We show that guarantee premiums are inexpensive, typically under 5% of the fare. Conditioning on the realized route roughly halves the premium while reducing tail risk. Analyzing membership abuse, we show that adverse selection acts precisely along the dimension the price fails to condition on, yielding a design principle: subsidies additive in the fare, such as a fixed per-ride discount, leave marginal incentives unchanged and are abuse-proof by construction, with deterministic closed-form cost.

stat.AP↗

arXiv2025

Technical overview and architecture of the FastNet Machine Learning weather prediction model, version 1.0

We present FastNet version 1.0, a data-driven medium range numerical weather prediction (NWP) model based on a Graph Neural Network architecture, developed jointly between the Alan Turing Institute and the Met Office. FastNet uses an encode-process-decode structure to produce deterministic global weather predictions out to 10 days. The architecture is independent of spatial resolution and we have trained models at 1$^{\circ}$ and 0.25$^{\circ}$ resolution, with a six hour time step. FastNet uses a multi-level mesh in the processor, which is able to capture both short-range and long-range patterns in the spatial structure of the atmosphere. The model is pre-trained on ECMWF's ERA5 reanalysis data and then fine-tuned on additional autoregressive rollout steps, which improves accuracy over longer time horizons. We evaluate the model performance at 1.5$^{\circ}$ resolution using 2022 as a hold-out year and compare with the Met Office Global Model, finding that FastNet surpasses the skill of the current Met Office Global Model NWP system using a variety of evaluation metrics on a number of atmospheric variables. Our results show that both our 1$^{\circ}$ and 0.25$^{\circ}$ FastNet models outperform the current Global Model and produce results with predictive skill approaching those of other data-driven models trained on 0.25$^{\circ}$ ERA5.

physics.ao-ph↗

arXiv2025

FastNet: Improving the physical consistency of machine-learning weather prediction models through loss function design

Machine learning weather prediction (MLWP) models have demonstrated remarkable potential in delivering accurate forecasts at significantly reduced computational cost compared to traditional numerical weather prediction (NWP) systems. However, challenges remain in ensuring the physical consistency of MLWP outputs, particularly in deterministic settings. This study presents FastNet, a graph neural network (GNN)-based global prediction model, and investigates the impact of alternative loss function designs on improving the physical realism of its forecasts. We explore three key modifications to the standard mean squared error (MSE) loss: (1) a modified spherical harmonic (MSH) loss that penalises spectral amplitude errors to reduce blurring and enhance small-scale structure retention; (2) inclusion of horizontal gradient terms in the loss to suppress non-physical artefacts; and (3) an alternative wind representation that decouples speed and direction to better capture extreme wind events. Results show that while the MSH and gradient-based losses \textit{alone} may slightly degrade RMSE scores, when trained in combination the model exhibits very similar MSE performance to an MSE-trained model while at the same time significantly improving spectral fidelity and physical consistency. The alternative wind representation further improves wind speed accuracy and reduces directional bias. Collectively, these findings highlight the importance of loss function design as a mechanism for embedding domain knowledge into MLWP models and advancing their operational readiness.

physics.ao-ph↗

arXiv2024

Gradient descent in matrix factorization: Understanding large initialization

Gradient Descent (GD) has been proven effective in solving various matrix factorization problems. However, its optimization behavior with large initial values remains less understood. To address this gap, this paper presents a novel theoretical framework for examining the convergence trajectory of GD with a large initialization. The framework is grounded in signal-to-noise ratio concepts and inductive arguments. The results uncover an implicit incremental learning phenomenon in GD and offer a deeper understanding of its performance in large initialization scenarios.

math.OC↗

arXiv2023

Parallel sampling of decomposable graphs using Markov chain on junction trees

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficulty in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a novel parallel non-reversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph. At every step, the parallel sampler executes simultaneously all edge perturbations within a partition. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current state-of-the-arts methods in terms of accuracy and computational efficiency. The implementation of our work is available in the Python package parallelDG.

stat.ME↗

arXiv2023

Predictive inference for travel time on transportation networks

Recent statistical methods fitted on large-scale GPS data can provide accurate estimations of the expected travel time between two points. However, little is known about the distribution of travel time, which is key to decision-making across a number of logistic problems. With sufficient data, single road-segment travel time can be well approximated. The challenge lies in understanding how to aggregate such information over a route to arrive at the route-distribution of travel time. We develop a novel statistical approach to this problem. We show that, under general conditions, without assuming a distribution of speed, travel time {divided by route distance follows a Gaussian distribution with route-invariant population mean and variance. We develop efficient inference methods for such parameters and propose asymptotically tight population prediction intervals for travel time. Using traffic flow information, we further develop a trip-specific Gaussian-based predictive distribution, resulting in tight prediction intervals for short and long trips. Our methods, implemented in an R-package, are illustrated in a real-world case study using mobile GPS data, showing that our trip-specific and population intervals both achieve the 95\% theoretical coverage levels. Compared to alternative approaches, our trip-specific predictive distribution achieves (a) the theoretical coverage at every level of significance, (b) tighter prediction intervals, (c) less predictive bias, and (d) more efficient estimation and prediction procedures. This makes our approach promising for low-latency, large-scale transportation applications.

stat.ME↗

arXiv2019

A hierarchical Bayesian model for predicting ecological interactions using scaled evolutionary relationships

Identifying undocumented or potential future interactions among species is a challenge facing modern ecologists. Recent link prediction methods rely on trait data, however large species interaction databases are typically sparse and covariates are limited to only a fraction of species. On the other hand, evolutionary relationships, encoded as phylogenetic trees, can act as proxies for underlying traits and historical patterns of parasite sharing among hosts. We show that using a network-based conditional model, phylogenetic information provides strong predictive power in a recently published global database of host-parasite interactions. By scaling the phylogeny using an evolutionary model, our method allows for biological interpretation often missing from latent variable models. To further improve on the phylogeny-only model, we combine a hierarchical Bayesian latent score framework for bipartite graphs that accounts for the number of interactions per species with the host dependence informed by phylogeny. Combining the two information sources yields significant improvement in predictive accuracy over each of the submodels alone. As many interaction networks are constructed from presence-only data, we extend the model by integrating a correction mechanism for missing interactions, which proves valuable in reducing uncertainty in unobserved interactions.

stat.AP↗

arXiv2017

Sub-clustering in decomposable graphs and size-varying junction trees

This paper proposes a novel representation of decomposable graphs based on semi-latent tree-dependent bipartite graphs. The novel representation has two main benefits. First, it enables a form of sub-clustering within maximal cliques of the graph, adding informational richness to the general use of decomposable graphs that could be harnessed in applications with behavioural type of data. Second, it allows for a new node-driven Markov chain Monte Carlo sampler of decomposable graphs that can easily parallelize and scale. The proposed sampler also benefits from the computational efficiency of junction-tree-based samplers of decomposable graphs.

stat.ME↗

arXiv2017

On decomposable random graphs

Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov update steps are thus remarkably simplified. Structural modelling with tree-dependent bipartite graphs has additional benefits. For example, certain properties that are hardly attainable in the decomposable form are now easily accessible. Moreover, tree-dependent bipartite graphs can extract and model extra information related to sub-clustering dynamics, while currently known models for decomposable graphs do not. Properties of decomposable graphs are also transferable to the expanded dimension, such as the attractive likelihood factorization property. As a result of using the bipartite representation, tools developed for random graphs can be used. Hence, a framework for random tree-dependent bipartite graphs, thereupon for random decomposable graphs, is proposed.

stat.ME↗

arXiv2017

A Skew-Normal Copula-Driven GLMM

This paper presents a method for fitting a copula-driven generalized linear mixed models. For added flexibility, the skew-normal copula is adopted for fitting. The correlation matrix of the skew-normal copula is used to capture the dependence structure within units, while the fixed and random effects coefficients are estimated through the mean of the copula. For estimation, a Monte Carlo expectation-maximization algorithm is developed. Simulations are shown alongside a real data example from the Framingham Heart Study.

stat.ME↗