We study dual volume sampling, a method for selecting k columns from an n*m short and wide matrix (n <= k <= m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix. This method was proposed by Avron and Boutsidis (2013), who showed it to be a promising method for column subset selection and its multiple applications. However, its wider adoption has been hampered by the lack of polynomial time sampling algorithms. We remove this hindrance by developing an exact (randomized) polynomial time sampling algorithm as well as its derandomization. Thereafter, we study dual volume sampling via the theory of real stable polynomials and prove that its distribution satisfies the "Strong Rayleigh" property. This result has numerous consequences, including a provably fast-mixing Markov chain sampler that makes dual volume sampling much more attractive to practitioners. This sampler is closely related to classical algorithms for popular experimental design methods that are to date lacking theoretical analysis but are known to empirically work well.

Your inner monologue may be less constant than you think--more like a fridge light that turns on when you look. Thinking doesn't always involve words. Breakthroughs, discoveries, and DIY tips sent six days a week. When I first started researching this story, I assumed I was writing about other people: those fascinating outliers who reportedly lack an internal monologue--the experience of actively speaking words in your mind as a sort of private narration of your life. Then I got on a Zoom call with Dr. Russell Hurlburt, a psychologist at the University of Nevada, Las Vegas, who has spent 50 years studying inner experience, and somewhere in the first ten minutes, I started to wonder: What if I'm talking about myself?

Aqara's Matter-compatible camera promises easier smart home integration The company says it's the first Matter-certified camera. Smart home company Aqara has launched what it says is the first camera certified for Matter, the open source standard that enables interoperability across brands, like Google and Amazon. The Aqara G350 is an indoor security cam that also functions as a Zigbee and Matter hub in the Aqara Home app, which means the camera will enable you to control various devices across smart home protocols from different brands within one location. The camera itself comes with a 4K wide-angle and a 2.5K telephoto lens, providing both panoramic and closeup views. It also has 9x hybrid zoom and a pan-tilt mechanism that can give you 360-degree coverage of the room it's in.

Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus allows us to handle noisy data well. However, since the t-exponential family is defined by the deformed exponential, an efficient learning algorithm for the t-exponential family such as expectation propagation (EP) cannot be derived in the same way as the ordinary exponential family. In this paper, we borrow the mathematical tools of q-algebra from statistical physics and show that the pseudo additivity of distributions allows us to perform calculation of t-exponential family distributions through natural parameters. We then develop an expectation propagation (EP) algorithm for the t-exponential family, which provides a deterministic approximation to the posterior or predictive distribution with simple moment matching. We finally apply the proposed EP algorithm to the Bayes point machine and Student-t process classification, and demonstrate their performance numerically.

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on a gradient-based update constructed to optimally decrease the KL divergence within a function space. This paper develops the first theoretical analysis on SVGD. We establish that the empirical measures of the SVGD samples weakly converge to the target distribution, and show that the asymptotic behavior of SVGD is characterized by a nonlinear Fokker-Planck equation known as Vlasov equation in physics. We develop a geometric perspective that views SVGD as a gradient flow of the KL divergence functional under a new metric structure on the space of distributions induced by Stein operator.

Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms called Uniform-PAC, which is a strengthening of the classical Probably Approximately Correct (PAC) framework. In contrast to the PAC framework, the uniform version may be used to derive high probability regret guarantees and so forms a bridge between the two setups that has been missing in the literature. We demonstrate the benefits of the new framework for finite-state episodic MDPs with a new algorithm that is Uniform-PAC and simultaneously achieves optimal regret and PAC guarantees except for a factor of the horizon.

Convolutional neural networks (CNNs) have recently been applied to the optical flow estimation problem. As training the CNNs requires sufficiently large ground truth training data, existing approaches resort to synthetic, unrealistic datasets. On the other hand, unsupervised methods are capable of leveraging real-world videos for training where the ground truth flow fields are not available. These methods, however, rely on the fundamental assumptions of brightness constancy and spatial smoothness priors which do not hold near motion boundaries. In this paper, we propose to exploit unlabeled videos for semi-supervised learning of optical flow with a Generative Adversarial Network. Our key insight is that the adversarial loss can capture the structural patterns of flow warp errors without making explicit assumptions. Extensive experiments on benchmark datasets demonstrate that the proposed semi-supervised algorithm performs favorably against purely supervised and semi-supervised learning schemes.

Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these conditions and generalize to a new one with few data? We present a new model called Latent Variable Multiple Output Gaussian Processes (LVMOGP) that allows to jointly model multiple conditions for regression and generalize to a new condition with a few data points at test time. LVMOGP infers the posteriors of Gaussian processes together with a latent space representing the information about different conditions. We derive an efficient variational inference method for LVMOGP for which the computational complexity is as low as sparse Gaussian processes. We show that LVMOGP significantly outperforms related Gaussian process methods on various tasks with both synthetic and real data.

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.

We address the problem of multi-class classification in the case where the number of classes is very large. We propose a double sampling strategy on top of a multi-class to binary reduction strategy, which transforms the original multi-class problem into a binary classification problem over pairs of examples. The aim of the sampling strategy is to overcome the curse of long-tailed class distributions exhibited in majority of large-scale multi-class classification problems and to reduce the number of pairs of examples in the expanded data. We show that this strategy does not alter the consistency of the empirical risk minimization principle defined over the double sample reduction. Experiments are carried out on DMOZ and Wikipedia collections with 10,000 to 100,000 classes where we show the efficiency of the proposed approach in terms of training and prediction time, memory consumption, and predictive performance with respect to state-of-the-art approaches.