Helge Kristian Jenssen

Simen Eide, Arnoldo Frigessi, Helge Jenssen et al.

We present a novel recommender systems dataset that records the sequential interactions between users and an online marketplace. The users are sequentially presented with both recommendations and search results in the form of ranked lists of items, called slates, from the marketplace. The dataset includes the presented slates at each round, whether the user clicked on any of these items and which item the user clicked on. Although the usage of exposure data in recommender systems is growing, to our knowledge there is no open large-scale recommender systems dataset that includes the slates of items presented to the users at each interaction. As a result, most articles on recommender systems do not utilize this exposure information. Instead, the proposed models only depend on the user's click responses, and assume that the user is exposed to all the items in the item universe at each step, often called uniform candidate sampling. This is an incomplete assumption, as it takes into account items the user might not have been exposed to. This way items might be incorrectly considered as not of interest to the user. Taking into account the actually shown slates allows the models to use a more natural likelihood, based on the click probability given the exposure set of items, as is prevalent in the bandit and reinforcement learning literature. \cite{Eide2021DynamicSampling} shows that likelihoods based on uniform candidate sampling (and similar assumptions) are implicitly assuming that the platform only shows the most relevant items to the user. This causes the recommender system to implicitly reinforce feedback loops and to be biased towards previously exposed items to the user.

Helge Kristian Jenssen, Trygve Karper

We establish existence of global-in-time weak solutions to the one dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas (pressure $p=Kθ/τ$, internal energy $e=c_v θ$), when the viscosity $μ$ is constant and the heat conductivity $κ$ depends on the temperature $θ$ according to $κ(θ) = \bar κθ^β$, with $0\leqβ<{3/2}$. This choice of degenerate transport coefficients is motivated by the kinetic theory of gasses. Approximate solutions are generated by a semi-discrete finite element scheme. We first formulate sufficient conditions that guarantee convergence to a weak solution. The convergence proof relies on weak compactness and convexity, and it applies to the more general constitutive relations $μ(θ) = \bar μθ^α$, $κ(θ) = \bar κθ^β$, with $α\geq 0$, $0 \leq β< 2$ ($\bar μ, \bar κ$ constants). We then verify the sufficient conditions in the case $α=0$ and $0\leqβ<{3/2}$. The data are assumed to be without vacuum, mass concentrations, or vanishing temperatures, and the same holds for the weak solutions.