Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by Dasgupta [12], and present two polynomial-time approximation algorithms: Our first result is an O(1)-approximation algorithm for graphs of high conductance. Our simple construction bypasses complicated recursive routines of finding sparse cuts known in the literature (e.g., [6, 11]). Our second and main result is an O(1)approximation algorithm for a wide family of graphs that exhibit a well-defined structure of clusters. This result generalises the previous state-of-the-art [10], which holds only for graphs generated from stochastic models. The significance of our work is demonstrated by the empirical analysis on both synthetic and real-world data sets, on which our presented algorithm outperforms the previously proposed algorithm for graphs with a well-defined cluster structure [10].

Evaluating observational estimators of causal effects demands information that is rarely available: unconfounded interventions and outcomes from the population of interest, created either by randomization or adjustment. As a result, it is customary to fall back on simulators when creating benchmark tasks. Simulators offer great control but are often too simplistic to make challenging tasks, either because they are hand-designed and lack the nuances of real-world data, or because they are fit to observational data without structural constraints. In this work, we propose a general, repeatable strategy for turning observational data into sequential structural causal models and challenging estimation tasks by following two simple principles: 1) fitting real-world data where possible, and 2) creating complexity by composing simple, hand-designed mechanisms. We implement these ideas in a highly configurable software package and apply it to the well-known Adult income data set to construct the IncomeSCM simulator. From this, we devise multiple estimation tasks and sample data sets to compare established estimators of causal effects. The tasks present a suitable challenge, with effect estimates varying greatly in quality between methods, despite similar performance in the modeling of factual outcomes, highlighting the need for dedicated causal estimators and model selection criteria.

Human image animation involves generating videos from a character photo, allowing user control and unlocking the potential for video and movie production. While recent approaches yield impressive results using high-quality training data, the inaccessibility of these datasets hampers fair and transparent benchmarking. Moreover, these approaches prioritize 2D human motion and overlook the significance of camera motions in videos, leading to limited control and unstable video generation. To demystify the training data, we present HumanVid, the first large-scale high-quality dataset tailored for human image animation, which combines crafted real-world and synthetic data. For the real-world data, we compile a vast collection of real-world videos from the internet. We developed and applied careful filtering rules to ensure video quality, resulting in a curated collection of 20K high-resolution (1080P) human-centric videos. Human and camera motion annotation is accomplished using a 2D pose estimator and a SLAM-based method. To expand our synthetic dataset, we collected 10K 3D avatar assets and leveraged existing assets of body shapes, skin textures and clothings. Notably, we introduce a rule-based camera trajectory generation method, enabling the synthetic pipeline to incorporate diverse and precise camera motion annotation, which can rarely be found in real-world data.

Their creators say it's the getting back up part that matters. A humanoid robot is carried by technicians after being knocked out in a kickboxing match at the World Humanoid Robot Games on August 15, 2025 in Beijing, China. Breakthroughs, discoveries, and DIY tips sent every weekday. Tech companies are collectively spending billions to turn the age old sci-fi trope of humanoid, general-purpose robots into reality. So far, that momentous effort has mostly produced staged performances, underwhelming demos, and of falling.