# On the (In)tractability of Computing Normalizing Constants for the Product of Determinantal Point Processes

We consider the product of determinantal point processes (DPPs), a point process whose probability mass is proportional to the product of principal minors of multiple matrices as a natural, promising generalization of DPPs.

# A Critical Reexamination of Intra-List Distance and Dispersion

no code implementations23 May 2023,

Diversification of recommendation results is a promising approach for coping with the uncertainty associated with users' information needs.

# Curse of "Low" Dimensionality in Recommender Systems

no code implementations23 May 2023,

Beyond accuracy, there are a variety of aspects to the quality of recommender systems, such as diversity, fairness, and robustness.

# Computational Complexity of Normalizing Constants for the Product of Determinantal Point Processes

no code implementations28 Nov 2021,

(2) $\sum_S\det({\bf A}_{S, S})\det({\bf B}_{S, S})\det({\bf C}_{S, S})$ is NP-hard to approximate within a factor of $2^{O(|I|^{1-\epsilon})}$ or $2^{O(n^{1/\epsilon})}$ for any $\epsilon>0$, where $|I|$ is the input size and $n$ is the order of the input matrix.

# Some Inapproximability Results of MAP Inference and Exponentiated Determinantal Point Processes

no code implementations2 Sep 2021

As a corollary of the first result, we demonstrate that the normalizing constant for E-DPPs of any (fixed) constant exponent $p \geq \beta^{-1} = 10^{10^{13}}$ is $\textsf{NP}$-hard to approximate within a factor of $2^{\beta pn}$, which is in contrast to the case of $p \leq 1$ admitting a fully polynomial-time randomized approximation scheme.

# Spanning Tree Constrained Determinantal Point Processes are Hard to (Approximately) Evaluate

no code implementations25 Feb 2021,

We consider determinantal point processes (DPPs) constrained by spanning trees.

# Predictive Optimization with Zero-Shot Domain Adaptation

no code implementations15 Jan 2021,

The task is regarded as predictive optimization, but existing predictive optimization methods have not been extended to handling multiple domains.

# Monotone k-Submodular Function Maximization with Size Constraints

A $k$-submodular function is a generalization of a submodular function, where the input consists of $k$ disjoint subsets, instead of a single subset, of the domain. Many machine learning problems, including influence maximization with $k$ kinds of topics and sensor placement with $k$ kinds of sensors, can be naturally modeled as the problem of maximizing monotone $k$-submodular functions. In this paper, we give constant-factor approximation algorithms for maximizing monotone $k$-submodular functions subject to several size constraints. The running time of our algorithms are almost linear in the domain size. We experimentally demonstrate that our algorithms outperform baseline algorithms in terms of the solution quality.

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