TPP models in density estimation and strongly outperforms them in forecasting.

How Does the Hive Mind Work in? The "Joining" seems to connect people via radio waves. Let's dig into the physics at play. Carol Sturka (left) and her chaperone," Zosia, in the Apple TV show . You know what's great about a show like?

Zelensky declares state of emergency in Ukraine's energy sector Ukraine has declared a state of emergency in the country's energy sector, with particular focus on Kyiv, as ongoing Russian strikes continue to leave thousands of residents without power. The nation is in the midst of a particularly cold winter, with overnight temperatures in Kyiv dropping to around -20C. After a special cabinet meeting, President Volodymyr Zelensky said a round-the-clock task force would be set up to deal with the damaging consequences of Russian airstrikes and worsening weather conditions. He accused Moscow of deliberately exploiting the harsh, sub-zero temperatures to target critical infrastructure, including energy distribution facilities. In recent weeks, Kyiv has been particularly affected by Russian attacks, leaving thousands of homes without regular power, heating or running water.

This paper discusses one of the most fundamental issues about point processes that what is the best sampling method for point processes. We propose \textit{thinning} as a downsampling method for accelerating the learning of point processes. We find that the thinning operation preserves the structure of intensity, and is able to estimate parameters with less time and without much loss of accuracy. Theoretical results including intensity, parameter and gradient estimation on a thinned history are presented for point processes with decouplable intensities. A stochastic optimization algorithm based on the thinned gradient is proposed.

In this paper, we tackle the Bayesian estimation of point process intensity as a function of covariates. We propose a novel augmentation of permanental process called augmented permanental process, a doubly-stochastic point process that uses a Gaussian process on covariate space to describe the Bayesian a priori uncertainty present in the square root of intensity, and derive a fast Bayesian estimation algorithm that scales linearly with data size without relying on either domain discretization or Markov Chain Monte Carlo computation. The proposed algorithm is based on a non-trivial finding that the representer theorem, one of the most desirable mathematical property for machine learning problems, holds for the augmented permanental process, which provides us with many significant computational advantages. We evaluate our algorithm on synthetic and real-world data, and show that it outperforms state-of-the-art methods in terms of predictive accuracy while being substantially faster than a conventional Bayesian method.

Sparse longitudinal (SL) textual data arises when individuals generate text repeatedly over time (e.g., customer reviews, occasional social media posts, electronic medical records across visits), but the frequency and timing of observations vary across individuals. These complex textual data sets have immense potential to inform future policy and targeted recommendations. However, because SL text data lack dedicated methods and are noisy, heterogeneous, and prone to anomalies, detecting and inferring key patterns is challenging. We introduce LLmFPCA-detect, a flexible framework that pairs LLM-based text embeddings with functional data analysis to detect clusters and infer anomalies in large SL text datasets. First, LLmFPCA-detect embeds each piece of text into an application-specific numeric space using LLM prompts. Sparse multivariate functional principal component analysis (mFPCA) conducted in the numeric space forms the workhorse to recover primary population characteristics, and produces subject-level scores which, together with baseline static covariates, facilitate data segmentation, unsupervised anomaly detection and inference, and enable other downstream tasks. In particular, we leverage LLMs to perform dynamic keyword profiling guided by the data segments and anomalies discovered by LLmFPCA-detect, and we show that cluster-specific functional PC scores from LLmFPCA-detect, used as features in existing pipelines, help boost prediction performance. We support the stability of LLmFPCA-detect with experiments and evaluate it on two different applications using public datasets, Amazon customer-review trajectories, and Wikipedia talk-page comment streams, demonstrating utility across domains and outperforming state-of-the-art baselines.