We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters. Group convolution layers are easy to use and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST.

The problem of cluster recovery under the stochastic block model has been intensely studied in statistics [24, 44, 6, 8, 47, 19], computer science (where it is known as the planted partition problem) [17, 25, 13, 31, 11, 12, 9, 4, 10], and theoretical statistical physics [14, 48, 15]. In the simplest binary form, the stochastic block model assumes that n vertices are partitioned into two clusters with edge probability a/n within the first cluster, c/n within the second cluster, and b/n across the two clusters. The goal is to reconstruct the underlying clusters from the observation of the graph. Different reconstruction goals can be considered depending on how the model parameters a, b, c scale with n (See [2] for more discussions): - Exact recovery (strong consistency). If the average degree is Ω(log n), it is possible to exactly recover the clusters (up to a permutation of cluster indices) with high probability.

The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the existing clustering ensemble approaches. Firstly, many approaches lack the ability to weight the base clusterings without access to the original data and can be affected significantly by the low-quality, or even ill clusterings. Secondly, they generally focus on the instance level or cluster level in the ensemble system and fail to integrate multi-granularity cues into a unified model. To address these two limitations, this paper proposes to solve the clustering ensemble problem via crowd agreement estimation and multigranularity link analysis. We present the normalized crowd agreement index (NCAI) to evaluate the quality of base clusterings in an unsupervised manner and thus weight the base clusterings in accordance with their clustering validity. To explore the relationship between clusters, the source aware connected triple (SACT) similarity is introduced with regard to their common neighbors and the source reliability. Present address: School of Information Science and Technology, Sun Yat-sen University, Guangzhou Higher Education Mega Center, Panyu District, Guangzhou, Guangdong, 510006, P. R. China. The experiments are conducted on eight real-world datasets. The experimental results demonstrate the effectiveness and robustness of the proposed methods. Keywords: Clustering ensemble, Clustering aggregation, Weighted evidence accumulation clustering, Graph partitioning with multi-granularity link analysis 1. Introduction Data clustering is a fundamental and very challenging problem in data mining and machine learning.

When random forests are used for binary classification, an ensemble of $t=1,2,\dots$ randomized classifiers is generated, and the predictions of the classifiers are aggregated by majority vote. Due to the randomness in the algorithm, there is a natural tradeoff between statistical performance and computational cost. On one hand, as $t$ increases, the (random) prediction error of the ensemble tends to decrease and stabilize. On the other hand, larger ensembles require greater computational cost for training and making new predictions. The present work offers a new approach for quantifying this tradeoff: Given a fixed training set $\mathcal{D}$, let the random variables $\text{Err}_{t,0}$ and $\text{Err}_{t,1}$ denote the class-wise prediction error rates of a randomly generated ensemble of size $t$. As $t\to\infty$, we provide a general bound on the "algorithmic variance", $\text{var}(\text{Err}_{t,l}|\mathcal{D})\leq \frac{f_l(1/2)^2}{4t}+o(\frac{1}{t})$, where $l\in\{0,1\}$, and $f_l$ is a density function that arises from the ensemble method. Conceptually, this result is somewhat surprising, because $\text{var}(\text{Err}_{t,l}|\mathcal{D})$ describes how $\text{Err}_{t,l}$ varies over repeated runs of the algorithm, and yet, the formula leads to a method for bounding $\text{var}(\text{Err}_{t,l}|\mathcal{D})$ with a single ensemble. The bound is also sharp in the sense that it is attained by an explicit family of randomized classifiers. With regard to the task of estimating $f_l(1/2)$, the presence of the ensemble leads to a unique twist on the classical setup of non-parametric density estimation --- wherein the effects of sample size and computational cost are intertwined. In particular, we propose an estimator for $f_l(1/2)$, and derive an upper bound on its MSE that matches "standard optimal non-parametric rates" when $t$ is sufficiently large.

Driving styles have a great influence on vehicle fuel economy, active safety, and drivability. To recognize driving styles of path-tracking behaviors for different divers, a statistical pattern-recognition method is developed to deal with the uncertainty of driving styles or characteristics based on probability density estimation. First, to describe driver path-tracking styles, vehicle speed and throttle opening are selected as the discriminative parameters, and a conditional kernel density function of vehicle speed and throttle opening is built, respectively, to describe the uncertainty and probability of two representative driving styles, e.g., aggressive and normal. Meanwhile, a posterior probability of each element in feature vector is obtained using full Bayesian theory. Second, a Euclidean distance method is involved to decide to which class the driver should be subject instead of calculating the complex covariance between every two elements of feature vectors. By comparing the Euclidean distance between every elements in feature vector, driving styles are classified into seven levels ranging from low normal to high aggressive. Subsequently, to show benefits of the proposed pattern-recognition method, a cross-validated method is used, compared with a fuzzy logic-based pattern-recognition method. The experiment results show that the proposed statistical pattern-recognition method for driving styles based on kernel density estimation is more efficient and stable than the fuzzy logic-based method.

Tribune Publishing, the parent company that owns several storied and proud newspapers in the US including the Chicago Tribune and the Los Angeles Times, announced on Thursday that it would be changing its name to "tronc Inc." In a press release, the company said that tronc Inc would be "a content curation and monetization company focused on creating and distributing premium, verified content across all channels". The name, according to the release, is a shortening of Tribune Online Content. "tronc pools the company's leading media brands and leverages innovative technology to deliver personalized and interactive experiences to its 60m monthly users," the release continued, using the lower-case t despite the word coming at the beginning of the sentence. The release also announced the launch of "troncX", an "online curation and monetization engine" which utilizes artificial intelligence technology "to accelerate digital growth".

After Thursday's annual shareholder meeting in downtown Los Angeles, LA Times' parent Tribune Publishing announced it would be changing its name to tronc Inc. and moving its shares from the New York Stock Exchange to the Nasdaq, effective June 20. In the release, the future consonant-heavy media organization describes itself as a "a content curation and monetization company focused on creating and distributing premium, verified content across all channels," or a news organization, in other words. It also "plans to launch www.tronc.com, "Our industry requires an innovative approach and a fundamentally different way of operating," Ferro said in the release. Earlier in the day, Tribune Chairman Michael Ferro won a big victory when he had his slate of board members confirmed.

The car horn has been described as'an instrument of torture' that is used to convey irritation. Now Google is teaching it's self-driving this trick, but says it will'be polite, considerate and only honk when it makes driving safer for everyone'. The search giant has been testing this application inside the car as a human took notes on when it was used, but the vehicles have been given the green light to honk at others on the road. Google is teaching it's self-driving how to honk, but says it will'be polite, considerate, and only honk when it makes driving safer for everyone'. Google has taught its self-driving cars how to honk at cars and others in the road, but it will'be polite, considerate, and only honk when it makes driving safer for everyone'.

The overall goal is to target treatment specifically to each individual so that clinical outcomes for that individual are optimized. One direction of attack is to use patient data to discover decision rules which specify the treatment to use as a function of a vector of features from the patient. Regression and classification are important statistical tools for estimating such rules based on either observational data or data from a randomized trial, and machine learning can help with this because of its ability to artfully handle high dimensional feature spaces with potentially complex interactions.

You could think of a hospital as a big cruise liner, afloat on a sea of data, charting and correcting course as the captain and crew read the shifting wave patterns, monitor their instruments, pump the bilge ... Put more prosaically, hospital executives have an awful lot of numbers to navigate while checking their dashboards and generating feedback internally and externally. Artificial intelligence technologies like machine discovery, machine learning and natural language generation are revolutionizing the performance of those tasks. It wasn't until the mid-1990s that the notion of comparing an organization's performance with results achieved by other organizations in the same business even entered the health care mindset. Today, the search term "hospital benchmarking" turns up 5,636 PubMed entries. Type those words into a search engine and you'll be deluged with URLs.