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.

In business, the acceleration of change means enterprises have to live in the future, not the present. Having the tools and technologies to enable forward-thinking and underpin digital transformation is key to survival. Supply chain procurement leaders are tasked with improving operational efficiencies and keeping an eye on the bottom line. For Raimundo Martinez, global digital solutions manager of procurement and supply chain at bp, the journey toward building a better supply chain starts with data. "So, today, everybody talks about AI, ML, and all these tools," says Martinez.

The growclusters package for R implements an enhanced version of k-means clustering that allows discovery of local clusterings or partitions for a collection of data sets that each draw their cluster means from a single, global partition. The package contains functions to estimate a partition structure for multivariate data. Estimation is performed under a penalized optimization derived from Bayesian non-parametric formulations. This paper describes some of the functions and capabilities of the growclusters package, including the creation of R Shiny applications designed to visually illustrate the operation and functionality of the growclusters package.

In the deeply interconnected world we live in, pieces of information link domains all around us. As graph databases embrace effectively relationships among data and allow processing and querying these connections efficiently, they are rapidly becoming a popular platform for storage that supports a wide range of domains and applications. As in the relational case, it is expected that data preserves a set of integrity constraints that define the semantic structure of the world it represents. When a database does not satisfy its integrity constraints, a possible approach is to search for a ‘similar’ database that does satisfy the constraints, also known as a repair. In this work, we study the problem of computing subset and superset repairs for graph databases with data values using a notion of consistency based on having a set of Reg-GXPath expressions as integrity constraints. We show that for positive fragments of Reg-GXPath these problems admit a polynomial-time algorithm, while the full expressive power of the language renders them intractable.

If you're dating and haven't found any success on the endless dating apps in the App Store, you may want to consider joining the group of singles using Instagram as a replacement. DMing (direct messaging) on the social platform--with over 1 billion monthly users--isn't new, but young people are now using it, and Instagram's newer app features, to find better dating success than from traditional dating apps. These Instagram users are not alone– successful celebrity couples like Joe Jonas and Sophie Turner, and Simone Biles and Jonathan Owens, haven't shied away from the fact they've connected via the platform's DMs. Even Meghan Markle wouldn't have become royalty had her friend not posted an Instagram photo of Markle that caught the attention of her now-husband, Prince Harry. Shooting your shot in the DMs can seem daunting, so here are some tips for flirting and dating via Instagram, according to the Gen Z users finding success with it.

The Monitor is a weekly column devoted to everything happening in the WIRED world of culture, from movies to memes, TV to Twitter. On Tuesday morning, Ruben Martinez Jr. was staring at his computer screen, calculating his chances. He was on a group chat trying to strategize the best way to score Taylor Swift tickets, and it was looking bleak. Everyone seemed to have 2,000-plus people ahead of them in line. Martinez, a software engineer at OkCupid, checked the browser developer tools to see if he could figure out his actual place in the queue. He thought he could find a percentage for how far back he was.

Any enterprise can unlock AI -- but only if leaders know how to actually leverage their data, define problems and iterate. In this VB On-Demand event, join industry experts as they dig into how enterprises can turn data into company-wide AI and machine learning solutions. Companies are foundering in the quest to realize AI objectives, not to mention a return on their investment in AI, and it comes down to the right data and the right expertise, says Paula Martinez, CEO and co-founder of Marvik, a machine learning consultancy. First, there's the expense and effort of uncovering good quality data from the mountain that's always growing, and labeling it properly to actually put analytics and machine learning developments into production. And then, going from proof of concept to a production-ready solution with quality standards that can be launched at scale is another enormous obstacle -- and a large part of that is finding a team with the right skills to carry out the task successfully.

Were you unable to attend Transform 2022? Check out all of the summit sessions in our on-demand library now! Making artificial intelligence (AI) work with humans requires having an internal data champion to help overcome fears and create a safe environment. That was the advice offered at Digital Procurement World in Amsterdam today in a session focused on combining humans and AI to help procurement become a top value driver in modern business. Working through overwhelming amounts of data and dealing with employee concerns that AI will take their jobs.

Silicon Valley is abuzz about artificial intelligence - software programs that can draw or illustrate or chat almost like a person. One Google engineer actually thought a computer program had gained sentience. A lot of AI experts, though, say there is no ghost in the machine. But what if it were true? That would introduce many legal and ethical questions.

In this paper we show that the problem of deciding the consistency of a knowledge base in the Description Logic ALCM is ExpTime-complete. The M stands for meta-modelling as defined by Motz, Rohrer and Severi. To show our main result, we define an ExpTime Tableau algorithm as an extension of an algorithm for ALC by Nguyen and Szalas.