This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural network-based estimator and derive a non-asymptotic convergence rate, decomposed into a training error, an approximation error, and a diffusion-related term scaling as ${\log N}/{N}$. For compositional drift functions, we establish an explicit rate. In the numerical experiments, we consider a drift function with local fluctuations generated by a double-layer compositional structure featuring local oscillations, and show that the empirical convergence rate becomes independent of the input dimension $d$. Compared to the $B$-spline method, the neural network estimator achieves better convergence rates and more effectively captures local features, particularly in higher-dimensional settings.

Methods for knowledge graph (KG) completion need to capture semantic regularities and use these regularities to infer plausible knowledge that is not explicitly stated. Most embedding-based methods are opaque in the kinds of regularities they can capture, although region-based KG embedding models have emerged as a more transparent alternative. By modeling relations as geometric regions in high-dimensional vector spaces, such models can explicitly capture semantic regularities in terms of the spatial arrangement of these regions. Unfortunately, existing region-based approaches are severely limited in the kinds of rules they can capture. We argue that this limitation arises because the considered regions are defined as the Cartesian product of two-dimensional regions. As an alternative, in this paper, we propose RESHUFFLE, a simple model based on ordering constraints that can faithfully capture a much larger class of rule bases than existing approaches. Moreover, the embeddings in our framework can be learned by a monotonic Graph Neural Network (GNN), which effectively acts as a differentiable rule base. This approach has the important advantage that embeddings can be easily updated as new knowledge is added to the KG. At the same time, since the resulting representations can be used similarly to standard KG embeddings, our approach is significantly more efficient than existing approaches to differentiable reasoning.

We explore the minimax optimal error associated with a demographic parity-constrained regression problem within the context of a linear model. Our proposed model encompasses a broader range of discriminatory bias sources compared to the model presented by Chzhen and Schreuder (2022). Our analysis reveals that the minimax optimal error for the demographic parity-constrained regression problem under our model is characterized by $\Theta(\frac{dM}{n})$, where $n$ denotes the sample size, $d$ represents the dimensionality, and $M$ signifies the number of demographic groups arising from sensitive attributes. Moreover, we demonstrate that the minimax error increases in conjunction with a larger bias present in the model.

Claire Denis's recent collaborations with the actress Juliette Binoche have all been modernist twists on classic genres, starting with "Let the Sunshine In," a screwball comedy, and "High Life," a work of science fiction. The latest, "Both Sides of the Blade," which opens Friday, is a romantic melodrama; it lays bare the societal circumstances that play a decisive role in a middle-aged couple's life together, and it does so without stinting on direct and passionate emotional expression. If melodrama is the art of exaggeration, presenting the lives of everyday people in the terms and the tone of tragedy, Denis approaches the genre as the art of democratic authenticity, of truth. She treats her characters' story like a mirror for the earnestness and the dignity with which they view themselves, and she displays the public conditions, the web of power and authority, that get in the way--and that are nonetheless inseparable from the way that they see themselves. There's something Edenic about the romance of Sara (Binoche) and Jean (Vincent Lindon), who are first seen frolicking and intertwining, playfully and passionately, in the sumptuous isolation of the sea.

Artificial intelligence (AI) is no longer the stuff of science fiction. The technology is already disrupting multiple industries, many of which impact you on a daily basis. Own an iPhone X? Its facial recognition system is powered by AI. Ever been redirected by Google Maps because of an accident or construction ahead? And those are just a couple of small examples.

Artificial intelligence is no longer the stuff of science fiction. The technology is already disrupting multiple industries, many of which impact you on a daily basis. Own an iPhone X? Its facial recognition system is powered by AI. Ever been redirected by Google Maps because of an accident or construction ahead? And those are just a couple of small examples.

Artificial intelligence (AI) is no longer the stuff of science fiction. The technology is already disrupting multiple industries, many of which impact you on a daily basis. Own an iPhone X? Its facial recognition system is powered by AI. Ever been redirected by Google Maps because of an accident or construction ahead? And those are just a couple of small examples.

Congrats and welcome to the throngs of creatives also tasked with publishing digital copy that resonates with both readers and robots to successfully catapult the brand ahead of the competition. Yes, it's a significant responsibility, particularly in our globally connected world where the search engine algorithms are constantly changing. However, going into the process armed with a few vital pointers and suggestions can quickly separate your posts and your brand from other industry players. Here are six tips to master editorial SEO basics for sustainable digital traction and return on investment. It's not enough to create compelling copy - you must strive to create compelling copy that your readers value.

Denis is Lead Technologist for IoT with Johnson Controls Innovation Group based in Cork, Ireland. His current role means collaborating extensively between technical and sales teams to drive further commercialisation opportunity through technology (both our own and partners/startups) into our sales channels, specifically looking at the emerging Smart Building market. The projects include our existing technologies – Building Security, Retail, HVAC and Building Energy - and emerging technologies such as IoT, AR and Machine Learning, then taking key input from numerous stakeholders and processes to deliver ROI for customers and partners from these solutions. Denis speaks on the national and international circuit for Johnson Controls at numerous technology conferences. Denis held a position of Principal Data Architect with EMC from 2010 to 2015, spending 2011 in Silicon Valley.

During his campaign for president, Donald Trump claimed Amazon was a monopoly he would go after for anti-trust violations if elected. Sure, Trump didn't like the coverage he was receiving in the Washington Post, which Amazon CEO Jeff Bezos owns. But even just judging by the latest holiday sales numbers, Amazon so decisively dominates online shopping that other retail giants can barely compete. If Trump decided to make good on his promise, should Bezos be worried? Amazon's dominance is just that: a company outdoing the competition in capitalism's grand tradition. If success alone were against the law, then yes.