The Expectation-Maximization (EM) algorithm is a widely used technique for parameter estimation. It is an iterative procedure that monotonically increases the likelihood. When the likelihood is not concave, it is well known that EM can converge to a non-global optimum. However, recent work has sidestepped the question of whether EM reaches the likelihood maximizer, instead by directly working out statistical guarantees on its loss. These 1 explorations have identified regions of initialization for which the EM estimate approaches the true parameter in probability, assuming the model is well-specified. This line of research was spurred by [1] which established general conditions for which a ball centered at the true parameter would be a basin of attraction for the population version of the EM operator. For a large enough sample size, the difference (in that ball) between the sample EM operator and the population EM operator can be bounded such that the EM estimate approaches the true parameter with high probability. That bound is the sum of two terms with distinct interpretations.

A significant literature studies ways of employing prior knowledge to improve power and precision of multiple testing procedures. Some common forms of prior knowledge may include (a) a priori beliefs about which hypotheses are null, modeled by non-uniform prior weights; (b) differing importances of hypotheses, modeled by differing penalties for false discoveries; (c) multiple arbitrary partitions of the hypotheses into known (possibly overlapping) groups, indicating (dis)similarity of hypotheses; and (d) knowledge of independence, positive or arbitrary dependence between hypotheses or groups, allowing for more aggressive or conservative procedures. We present a unified algorithmic framework called p-filter for global null testing and false discovery rate (FDR) control that allows the scientist to incorporate all four types of prior knowledge (a)-(d) simultaneously, recovering a wide variety of common algorithms as special cases.

We propose and systematically evaluate three strategies for training dynamically-routed artificial neural networks: graphs of learned transformations through which different input signals may take different paths. Though some approaches have advantages over others, the resulting networks are often qualitatively similar. We find that, in dynamically-routed networks trained to classify images, layers and branches become specialized to process distinct categories of images. Additionally, given a fixed computational budget, dynamically-routed networks tend to perform better than comparable statically-routed networks.

Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on the tangent bundle. As a result, we can construct a distance in this class which leads to a pre-compactness theorem on the class under consideration.

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The computational effort can be large, especially when ab initio or electron density functional calculations are used to evaluate the energy and atomic forces. Here, we show how the number of such evaluations can be reduced by an order of magnitude using a Gaussian process regression approach where an approximate energy surface is generated and refined in each iteration. When the goal is to evaluate the transition rate within harmonic transition state theory, the evaluation of the Hessian matrix at the initial and final state minima can be carried out beforehand and used as input in the minimum energy path calculation, thereby improving stability and reducing the number of iterations needed for convergence. A Gaussian process model also provides an uncertainty estimate for the approximate energy surface, and this can be used to focus the calculations on the lesser-known part of the path, thereby reducing the number of needed energy and force evaluations to a half in the present calculations. The methodology is illustrated using the two-dimensional M\"uller-Brown potential surface and performance assessed on an established benchmark involving 13 rearrangement transitions of a heptamer island on a solid surface.

Deep learning algorithms have recently produced state-of-the-art accuracy in many classification tasks, but this success is typically dependent on access to many annotated training examples. For domains without such data, an attractive alternative is to train models with light, or distant supervision. In this paper, we introduce a deep neural network for the Learning from Label Proportion (LLP) setting, in which the training data consist of bags of unlabeled instances with associated label distributions for each bag. We introduce a new regularization layer, Batch Averager, that can be appended to the last layer of any deep neural network to convert it from supervised learning to LLP. This layer can be implemented readily with existing deep learning packages. To further support domains in which the data consist of two conditionally independent feature views (e.g. image and text), we propose a co-training algorithm that iteratively generates pseudo bags and refits the deep LLP model to improve classification accuracy. We demonstrate our models on demographic attribute classification (gender and race/ethnicity), which has many applications in social media analysis, public health, and marketing. We conduct experiments to predict demographics of Twitter users based on their tweets and profile image, without requiring any user-level annotations for training. We find that the deep LLP approach outperforms baselines for both text and image features separately. Additionally, we find that co-training algorithm improves image and text classification by 4% and 8% absolute F1, respectively. Finally, an ensemble of text and image classifiers further improves the absolute F1 measure by 4% on average.

Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a sampling set non-trivial and hard to analyze. Indeed, though conditions for graph signal interpolation from noiseless samples exist, they do not lead to a unique sampling set. The presence of noise makes choosing among these sampling sets a hard combinatorial problem. Although greedy sampling schemes are commonly used in practice, they have no performance guarantee. This work takes a twofold approach to address this issue. First, universal performance bounds are derived for the Bayesian estimation of graph signals from noisy samples. In contrast to currently available bounds, they are not restricted to specific sampling schemes and hold for any sampling sets. Second, this paper provides near-optimal guarantees for greedy sampling by introducing the concept of approximate submodularity and updating the classical greedy bound. It then provides explicit bounds on the approximate supermodularity of the interpolation mean-square error showing that it can be optimized with worst-case guarantees using greedy search even though it is not supermodular. Simulations illustrate the derived bound for different graph models and show an application of graph signal sampling to reduce the complexity of kernel principal component analysis.

Concept Trees are a type of database that can organise arbitrary textual information using a very simple rule. Each tree tries to represent a single cohesive concept and the trees can link with each other for navigation and semantic purposes. The trees are therefore a type of semantic network and would benefit from having a consistent level of context for each of the nodes. The Concept Tree nodes have a mathematical basis allowing for a consistent build process. These would represent nouns or verbs in a text sentence, for example. New to the design can then be lists of descriptive elements for each of the nodes. The descriptors can also be weighted, but do not have to follow the strict counting rule of the tree nodes. With the new descriptive layers, a much richer type of knowledge can be achieved and still reasoned over automatically. The linking structure of the licas network is very relevant to building the concept trees now and forms the basis for their construction. The concept tree - symbolic neural network relation is also extended further.

This is the controversial AI computer program that researchers claim can determine if someone is gay or not just by looking at a photograph of their face. According to the Stanford University researchers who developed it, the artificial intelligence system can infer someone's sexuality with up to 91 percent accuracy by scanning a photograph of a man or woman. But critics have slammed the software, saying it could be used to'out' men and women currently in the closet. Software was used to make composite faces. On left are faces'least likely' to be homosexual, and center are faces'most likely' to be homosexual.

If you're hoping to turn up the heat in the bedroom, you may want to put on Marvin Gaye's 1983 chart-topper, Sexual Healing. A new study has shown that our sense of touch is heightened while listening to'sexy' songs. The researchers suggest that music's relation to touch may have played a key role in our evolution as a species, as song preference brought certain individuals together to mate. If you're hoping to turn up the heat in the bedroom, you may want to put on Marvin Gaye's 1983 chart-topper, Sexual Healing. A new study has shown that our sense of touch is heightened while listening to'sexy' songs (stock image) To understand the effect of sexy music, the researchers enlisted the help of a robot.