Pair correlation functions and limiting distributions of iterated cluster point processes

We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier work by Felsenstein and Shimatani describing a reproducing population. We discuss when closed term expressions of the first and second order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument

Functional summary statistics for point processes on the sphere with an application to determinantal point processes

We study point processes on $\mathbb S^d$, the $d$-dimensional unit sphere $\mathbb S^d$, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case $d=2$. The first part studies reduced Palm distributions and functional summary statistics, including nearest neighbour functions, empty space functions, and Ripley's and inhomogeneous $K$-functions. The second part partly discusses the appealing properties of determinantal point process (DPP) models on the sphere and partly considers the application of functional summary statistics to DPPs. In fact DPPs exhibit repulsiveness, but we also use them together with certain dependent thinnings when constructing point process models on the sphere with aggregation on the large scale and regularity on the small scale. We conclude with a discussion on future work on statistics for spatial point processes on the sphere

Mind the Gap: A Generative Approach to Interpretable Feature Selection and Extraction

We present the Mind the Gap Model (MGM), an approach for interpretable feature extraction and selection. By placing interpretability criteria directly into the model, we allow for the model to both optimize parameters related to interpretability and to directly report a global set of distinguishable dimensions to assist with further data exploration and hypothesis generation. MGM extracts distinguishing features on real-world datasets of animal features, recipes ingredients, and disease co-occurrence. It also maintains or improves performance when compared to related approaches. We perform a user study with domain experts to show the MGM's ability to help with dataset explorationNational Science Foundation (U.S.) (ACI 1544628

Query-Focused Video Summarization: Dataset, Evaluation, and A Memory Network Based Approach

Recent years have witnessed a resurgence of interest in video summarization. However, one of the main obstacles to the research on video summarization is the user subjectivity - users have various preferences over the summaries. The subjectiveness causes at least two problems. First, no single video summarizer fits all users unless it interacts with and adapts to the individual users. Second, it is very challenging to evaluate the performance of a video summarizer. To tackle the first problem, we explore the recently proposed query-focused video summarization which introduces user preferences in the form of text queries about the video into the summarization process. We propose a memory network parameterized sequential determinantal point process in order to attend the user query onto different video frames and shots. To address the second challenge, we contend that a good evaluation metric for video summarization should focus on the semantic information that humans can perceive rather than the visual features or temporal overlaps. To this end, we collect dense per-video-shot concept annotations, compile a new dataset, and suggest an efficient evaluation method defined upon the concept annotations. We conduct extensive experiments contrasting our video summarizer to existing ones and present detailed analyses about the dataset and the new evaluation method

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties