When viewed on a cosmic scale, humanity lives on a tiny grain of sand floating in an unimaginably-deep ocean. Huge expanses of space separate even the closest stars, ensuring that, should any sufficiently intelligent life form want to spread across the galaxy, it would take a momentous effort to launch across the interstellar seas. As we look toward the stars, hoping that we may visit them some day, many would argue that interstellar travel is impossible. After all, the nearest-known star system is over 4 light-years away. Let's think about that for a moment: It takes light 8 minutes and 20 seconds to travel from the sun's surface to our planet's atmosphere.

Let ${\mathcal S}_m$ be the set of all $m\times m$ density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix $\rho\in {\mathcal S}_m$ based on outcomes of $n$ measurements of observables $X_1,\dots, X_n\in {\mathbb H}_m$ (${\mathbb H}_m$ being the space of $m\times m$ Hermitian matrices) for a quantum system identically prepared $n$ times in state $\rho.$ Outcomes $Y_1,\dots, Y_n$ of such measurements could be described by a trace regression model in which ${\mathbb E}_{\rho}(Y_j|X_j)={\rm tr}(\rho X_j), j=1,\dots, n.$ The design variables $X_1,\dots, X_n$ are often sampled at random from the uniform distribution in an orthonormal basis $\{E_1,\dots, E_{m^2}\}$ of ${\mathbb H}_m$ (such as Pauli basis). The goal is to estimate the unknown density matrix $\rho$ based on the data $(X_1,Y_1), \dots, (X_n,Y_n).$ Let $$ \hat Z:=\frac{m^2}{n}\sum_{j=1}^n Y_j X_j $$ and let $\check \rho$ be the projection of $\hat Z$ onto the convex set ${\mathcal S}_m$ of density matrices. It is shown that for estimator $\check \rho$ the minimax lower bounds in classes of low rank density matrices (established earlier) are attained up logarithmic factors for all Schatten $p$-norm distances, $p\in [1,\infty]$ and for Bures version of quantum Hellinger distance. Moreover, for a slightly modified version of estimator $\check \rho$ the same property holds also for quantum relative entropy (Kullback-Leibler) distance between density matrices.

Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or in some stronger sense to the Bayes risk or to the Bayes decision function. Kernel methods based on minimizing the regularized risk over a reproducing kernel Hilbert space (RKHS) belong to these statistical machine learning methods. It is in general unknown which kernel yields optimal results for a particular data set or for the unknown probability measure. Hence various kernel learning methods were proposed to choose the kernel and therefore also its RKHS in a data adaptive manner. Nevertheless, many practitioners often use the classical Gaussian RBF kernel or certain Sobolev kernels with good success. The goal of this short note is to offer one possible theoretical explanation for this empirical fact.

We study the minimization of a convex function $f(X)$ over the set of $n\times n$ positive semi-definite matrices, but when the problem is recast as $\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq n$. We study the performance of gradient descent on $g$---which we refer to as Factored Gradient Descent (FGD)---under standard assumptions on the original function $f$. We provide a rule for selecting the step size and, with this choice, show that the local convergence rate of FGD mirrors that of standard gradient descent on the original $f$: i.e., after $k$ steps, the error is $O(1/k)$ for smooth $f$, and exponentially small in $k$ when $f$ is (restricted) strongly convex. In addition, we provide a procedure to initialize FGD for (restricted) strongly convex objectives and when one only has access to $f$ via a first-order oracle; for several problem instances, such proper initialization leads to global convergence guarantees. FGD and similar procedures are widely used in practice for problems that can be posed as matrix factorization. To the best of our knowledge, this is the first paper to provide precise convergence rate guarantees for general convex functions under standard convex assumptions.

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.

This paper addresses the problem of localizing audio sources using binaural measurements. We propose a supervised formulation that simultaneously localizes multiple sources at different locations. The approach is intrinsically efficient because, contrary to prior work, it relies neither on source separation, nor on monaural segregation. The method starts with a training stage that establishes a locally-linear Gaussian regression model between the directional coordinates of all the sources and the auditory features extracted from binaural measurements. While fixed-length wide-spectrum sounds (white noise) are used for training to reliably estimate the model parameters, we show that the testing (localization) can be extended to variable-length sparse-spectrum sounds (such as speech), thus enabling a wide range of realistic applications. Indeed, we demonstrate that the method can be used for audio-visual fusion, namely to map speech signals onto images and hence to spatially align the audio and visual modalities, thus enabling to discriminate between speaking and non-speaking faces. We release a novel corpus of real-room recordings that allow quantitative evaluation of the co-localization method in the presence of one or two sound sources. Experiments demonstrate increased accuracy and speed relative to several state-of-the-art methods.

New lip-reading technology developed at the University of East Anglia could help in solving crimes and provide communication assistance for people with hearing and speech impairments. The visual speech recognition technology, created by Helen L. Bear, PhD, and Prof Richard Harvey of UEA's School of Computing Sciences, can be applied "any place where the audio isn't good enough to determine what people are saying," Bear said. Those include criminal investigations, entertainment, and especially where are there are high levels of noise, such as in cars or aircraft cockpits, she said. Bear said unique problems with determining speech arise when sound isn't available -- such as on video footage -- or if the audio is inadequate and there aren't clues to give the context of a conversation. The sounds '/p/,' '/b/,' and '/m/' all look similar on the lips, but now the machine lip-reading classification technology can differentiate between the sounds for a more accurate translation.

Vast swarms of miniature robots are coming -- and they might be the answer to scrubbing our waters clean of lead. "Microbots" smaller than the width of a human hair could be highly effective and cost-efficient tools for removing lead and other contaminants from industrial wastewater, according to a new study published in the journal Nano Letters last month. In the space of a single hour, the study showed, self-propelled microbots could remove up to 95 percent of lead from water. Lead is commonly found in wastewater from mines or factories that make batteries and electronic devices, and can pose a serious risk to public health, as the water crisis in Flint, Michigan demonstrates. Heavy metal pollution can cost big cities billions of dollars a year, said Samuel Sánchez, co-author of the study and a research group leader at the Max Planck Institute for Intelligent Systems in Germany.

A blockchain intelligence vendor focused on combining the technology used to record and verify transactions with big data and artificial intelligence has attracted a pair of top technologist to serve in senior positions. Skry Inc., formerly Coinalytics, unveiled a name change this week along with the addition of new CTO and chief data scientist. The block chain analytics and intelligence firm based in Silicon Valley said Akash Singh, former CTO for data science at Chinese telecommunications giant Huawei (SHE: 002502) will serve as Skry's CTO. Singh also worked at IBM (NYSE: IBM), contributing to the development of its Watson cognitive computing platform. Also joining Skry is artificial intelligence researcher Masoud Nikravesh, former director of computational science and engineering at the University of California at Berkeley's Center for Information Technology Research in the Interest of Society.

Mark Zuckerberg wants to overtake Elon Musk to become the real-world version of Marvel superhero Tony Stark. The billionaire Facebook founder has expressed his desire (in a Facebook post, of course) to spend 2016 building an artificially intelligent assistant to help run his life at home and work – and directly compared it to Jarvis, the AI companion developed by Stark in the Iron Man films. Previous aims have included spending a year eating only meat from animals he killed himself in 2011, to read two books a month in 2015, and to learn Mandarin in a year in 2010. And when he declares one of the challenges, he goes hard on it: in October last year, he showed off his language abilities, delivering a 20-minute speech to students at Beijing's Tsinghua University entirely in Mandarin. Zuckerberg will start the project by "exploring what technology is already out there". Existing home-automation tools from companies such as Google's Nest, Phillips and Samsung all allow a fairly high level of control of a "smart home", and can be paired with voice control software, including that from Apple, Amazon and Massachusetts-based specialists Nuance.