This intriguing phenomenon, where the two asymptotics are equal, was rigorously justified by the seminal work on Le Cam equivalence. These work established the asymptotic equivalence between Gaussian sequence models, the white noise model, and certain nonparametric regression models (see, e.g., [3, 4, 5]). Since then, subsequent studies have established similar exact risks for a variety of nonparametric estimation problems. These include density estimation, regression models with non-Gaussian noise or random designs, analysis of Besov bodies, and wavelet estimation (e.g., [6, 7, 8, 2, 9, 10, 11, 12, 13]). For a detailed review of these developments, one can refer to [14] and the references therein. Constants akin to β(m, R), now often referred to as the Pinsker constant, play an indispensable role in studying the super-efficiency phenomenon observed in nonparametric problems. This phenomenon has been the subject of extensive investigation (e.g., [15, 16, 17, 18]). Recently, the strong theoretical links between the training dynamics within wide neural networks and the corresponding neural tangent kernel in regression have motivated substantial research into understanding the performance of spectral algorithms, such as kernel ridge regression and kernel gradient descent, in the context of kernel regression problems (see, e.g., [19, 20, 21, 22, 23, 24]).

The past decade has seen the democratization of photography through the smartphone revolution, with more pictures taken every two minutes than were taken throughout the entirety of the 1800s, according to some estimates. In fact, InfoTrends predicts more than a trillion images will be taken this year alone. "Cameras generate so much data, and a lot of times you need immediate action and analysis from this data," she says. "This research area is one that I'm very passionate about and its increasingly becoming more important to HP." Lin and her team were the creators of Pixel Intelligence, a powerful portfolio of computer vision algorithms that helps print service providers make sense of visual data. The algorithms can find faces within an image or find the same face in multiple images with great accuracy.