Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, treating successive graph signals independently or taking a global average. To address this shortcoming, this paper considers the statistical analysis of time-varying graph signals. We introduce a novel definition of joint (time-vertex) stationarity, which generalizes the classical definition of time stationarity and the more recent definition appropriate for graphs. Joint stationarity gives rise to a scalable Wiener optimization framework for joint denoising, semi-supervised learning, or more generally inversing a linear operator, that is provably optimal. Experimental results on real weather data demonstrate that taking into account graph and time dimensions jointly can yield significant accuracy improvements in the reconstruction effort.

In this paper we model the problem of learning preferences of a population as an active learning problem. We propose an algorithm can adaptively choose pairs of items to show to users coming from a heterogeneous population, and use the obtained reward to decide which pair of items to show next. We provide computationally efficient algorithms with provable sample complexity guarantees for this problem in both the noiseless and noisy cases. In the process of establishing sample complexity guarantees for our algorithms, we establish new results using a Nystr{\"o}m-like method which can be of independent interest. We supplement our theoretical results with experimental comparisons.

It is known that for a certain class of single index models (SIMs) $Y = f(\boldsymbol{X}_{p \times 1}^\intercal\boldsymbol{\beta}_0, \varepsilon)$, support recovery is impossible when $\boldsymbol{X} \sim \mathcal{N}(0, \mathbb{I}_{p \times p})$ and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design $\boldsymbol{X}$ comes from an i.i.d. Gaussian distribution. In the present paper we analyze algorithms based on covariance screening and least squares with $L_1$ penalization (i.e. LASSO) and demonstrate that they can also enjoy optimal (up to a scalar) rescaled sample size in terms of support recovery, albeit under slightly different assumptions on $f$ and $\varepsilon$ compared to the SIR based algorithms. Furthermore, we show more generally, that LASSO succeeds in recovering the signed support of $\boldsymbol{\beta}_0$ if $\boldsymbol{X} \sim \mathcal{N}(0, \boldsymbol{\Sigma})$, and the covariance $\boldsymbol{\Sigma}$ satisfies the irrepresentable condition. Our work extends existing results on the support recovery of LASSO for the linear model, to a more general class of SIMs.

In this paper we study the support recovery problem for single index models $Y=f(\boldsymbol{X}^{\intercal} \boldsymbol{\beta},\varepsilon)$, where $f$ is an unknown link function, $\boldsymbol{X}\sim N_p(0,\mathbb{I}_{p})$ and $\boldsymbol{\beta}$ is an $s$-sparse unit vector such that $\boldsymbol{\beta}_{i}\in \{\pm\frac{1}{\sqrt{s}},0\}$. In particular, we look into the performance of two computationally inexpensive algorithms: (a) the diagonal thresholding sliced inverse regression (DT-SIR) introduced by Lin et al. (2015); and (b) a semi-definite programming (SDP) approach inspired by Amini & Wainwright (2008). When $s=O(p^{1-\delta})$ for some $\delta>0$, we demonstrate that both procedures can succeed in recovering the support of $\boldsymbol{\beta}$ as long as the rescaled sample size $\kappa=\frac{n}{s\log(p-s)}$ is larger than a certain critical threshold. On the other hand, when $\kappa$ is smaller than a critical value, any algorithm fails to recover the support with probability at least $\frac{1}{2}$ asymptotically. In other words, we demonstrate that both DT-SIR and the SDP approach are optimal (up to a scalar) for recovering the support of $\boldsymbol{\beta}$ in terms of sample size. We provide extensive simulations, as well as a real dataset application to help verify our theoretical observations.

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the fitted estimating equations to a sparse direction obtained by solving a large-scale linear program. Our main theoretical contribution is to establish a unified Z-estimation theory of confidence regions for high dimensional problems. Different from existing methods, all of which require the specification of the likelihood or pseudo-likelihood, our framework is likelihood-free. As a result, our approach provides valid inference for a broad class of high dimensional constrained estimating equation problems, which are not covered by existing methods. Such examples include, noisy compressed sensing, instrumental variable regression, undirected graphical models, discriminant analysis and vector autoregressive models. We present detailed theoretical results for all these examples. Finally, we conduct thorough numerical simulations, and a real dataset analysis to back up the developed theoretical results.

Europe's growing army of robot workers could be classed as'electronic persons' and their owners liable to paying social security for them if the European Union adopts a draft plan to address the realities of a new industrial revolution. Robots are being deployed in ever-greater numbers in factories and also taking on tasks such as personal care or surgery, raising fears over unemployment, wealth inequality and alienation. Their growing intelligence, pervasiveness and autonomy requires rethinking everything from taxation to legal liability, a draft European Parliament motion, dated May 31, suggests. Europe's growing army of robot workers could be classed as'electronic persons' and their owners liable to paying social security under a draft EU proposal. The draft motion called on the European Commission to consider'that at least the most sophisticated autonomous robots could be established as having the status of electronic persons with specific rights and obligations'.

A few hundred miles south of Tesla Motors headquarters resides another electric car maker that has been given the green-light to unleash its prototypes on California roads. Faraday Future won approval today from The Golden State to begin testing its self-driving vehicles later this year on public routes. The Los Angeles-based startup plans to start building and selling electric vehicles next year in the United States, but has not disclosed details of regarding its newly awarded self-driving program. Faraday Future won approval today from The Golden State to begin testing its self-driving electric vehicles later this year on public routes. Faraday is one of several Chinese-funded startups hoping to challenge Tesla in premium electric vehicles.

Flying a drone for commercial purposes will no longer require a pilot's license, the Federal Aviation Administration announced in new rules released Tuesday. Drones flown in for-profit uses will no longer require a special permit so long as they weigh no more than 55 pounds, soar no higher than 400 feet and fly no closer than 400 feet from buildings or structures, the guidelines stipulate. Previous rules required commercial drone operators to have a pilot's license and apply for an FAA waiver – a tedious process believed to have steered many businesses to use drones without proper permission. The new regulation, which takes effect in August, will allow anyone over the age of 16 to fly a commercial drone so long as they apply for a remote pilot certificate, which requires passing an aeronautics test at an FAA-approved facility and undergoing a background check. That threshold is far lower than a pilot's license – a move likely to encourage greater commercial use of drones, industry experts predict.

If you're lucky enough to get a ticket to this year's Wimbledon tennis championships, be prepared to be scanned by a supercomputer. Cameras linked to IBM's Watson "machine-learning" platform may be monitoring your facial expressions and trying to work out what emotions you are displaying. If Watson learns quickly enough over the fortnight, it will apparently be able to work out which player you are supporting just by reading your face. The All England Lawn Tennis Club (AELTC) and its tech partner IBM are remaining tight-lipped on the details of the new technology - not least because it needs legal approval and raises privacy concerns. But it is another example of how sport is becoming increasingly digital, for fans, players and venues alike. Even if Watson isn't tracking your every cheer and grimace at the championships - which begin on Monday 27 June - it will be digesting millions of conversations on social media platforms, such as Twitter, Facebook and Instagram, and using natural language processing to identify common topics - not necessarily just about tennis.

As sensors are attached to more and more industrial machines, these connected devices create a massive glut of data. But to unleash the true value of Internet of Things (IoT) data analysis, businesses need to have a clear understanding of its strengths and weaknesses. In a panel discussion at the 2016 IoT Data Analytics & Visualization conference in Palo Alto, Calif., several speakers said the most important thing to keep in mind is that the industrial Internet should be about improving business processes, not just about implementing cool new technology. Nauman Sheikh, founder and CEO of analytics consulting firm Asrym Inc., said he recently worked with a large public utility to put sensors on maintenance trucks to do predictive maintenance. Sheikh built the predictive models that analyzed the data coming from the sensors to identify vibration patterns and other signs that a truck might be at risk of breaking down.