In the variational relevance vector machine, the gamma distribution is representative as a hyperprior over the noise precision of automatic relevance determination prior. Instead of the gamma hyperprior, we propose to use the inverse gamma hyperprior with a shape parameter close to zero and a scale parameter not necessary close to zero. This hyperprior is associated with the concept of a weakly informative prior. The effect of this hyperprior is investigated through regression to non-homogeneous data. Because it is difficult to capture the structure of such data with a single kernel function, we apply the multiple kernel method, in which multiple kernel functions with different widths are arranged for input data. We confirm that the degrees of freedom in a model is controlled by adjusting the scale parameter and keeping the shape parameter close to zero. A candidate for selecting the scale parameter is the predictive information criterion. However the estimated model using this criterion seems to cause over-fitting. This is because the multiple kernel method makes the model a situation where the dimension of the model is larger than the data size. To select an appropriate scale parameter even in such a situation, we also propose an extended prediction information criterion. It is confirmed that a multiple kernel relevance vector regression model with good predictive accuracy can be obtained by selecting the scale parameter minimizing extended prediction information criterion.

We present SmartExchange, an algorithm-hardware co-design framework to trade higher-cost memory storage/access for lower-cost computation, for energy-efficient inference of deep neural networks (DNNs). We develop a novel algorithm to enforce a specially favorable DNN weight structure, where each layerwise weight matrix can be stored as the product of a small basis matrix and a large sparse coefficient matrix whose non-zero elements are all power-of-2. To our best knowledge, this algorithm is the first formulation that integrates three mainstream model compression ideas: sparsification or pruning, decomposition, and quantization, into one unified framework. The resulting sparse and readily-quantized DNN thus enjoys greatly reduced energy consumption in data movement as well as weight storage. On top of that, we further design a dedicated accelerator to fully utilize the SmartExchange-enforced weights to improve both energy efficiency and latency performance. Extensive experiments show that 1) on the algorithm level, SmartExchange outperforms state-of-the-art compression techniques, including merely sparsification or pruning, decomposition, and quantization, in various ablation studies based on nine DNN models and four datasets; and 2) on the hardware level, the proposed SmartExchange based accelerator can improve the energy efficiency by up to 6.7$ imes$ and the speedup by up to 19.2$ imes$ over four state-of-the-art DNN accelerators, when benchmarked on seven DNN models (including four standard DNNs, two compact DNN models, and one segmentation model) and three datasets.

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate exact gradient of log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), which is much faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results are compared with CD. The classification accuracy results indicate similar performance of both methods. Image reconstruction as well as log-likelihood calculations are used to compare the performance of quantum and classical algorithms for RBM training. It is shown that the samples obtained from quantum annealer can be used to train a RBM on a 64-bit `bars and stripes' data set with classification performance similar to a RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer eliminates computationally expensive MCMC steps of CD.

Hierarchical Agglomerative Clustering (HAC) algorithms are extensively utilized in modern data science and machine learning, and seek to partition the dataset into clusters while generating a hierarchical relationship between the data samples themselves. HAC algorithms are employed in a number of applications, such as biology, natural language processing, and recommender systems. Thus, it is imperative to ensure that these algorithms are fair-- even if the dataset contains biases against certain protected groups, the cluster outputs generated should not be discriminatory against samples from any of these groups. However, recent work in clustering fairness has mostly focused on center-based clustering algorithms, such as k-median and k-means clustering. Therefore, in this paper, we propose fair algorithms for performing HAC that enforce fairness constraints 1) irrespective of the distance linkage criteria used, 2) generalize to any natural measures of clustering fairness for HAC, 3) work for multiple protected groups, and 4) have competitive running times to vanilla HAC. To the best of our knowledge, this is the first work that studies fairness for HAC algorithms. We also propose an algorithm with lower asymptotic time complexity than HAC algorithms that can rectify existing HAC outputs and make them subsequently fair as a result. Moreover, we carry out extensive experiments on multiple real-world UCI datasets to demonstrate the working of our algorithms.

An important component of every country's COVID-19 response is fast and efficient testing -- to identify and isolate cases, as well as for early detection of local hotspots. For many countries, producing a sufficient number of tests has been a serious limiting factor in their efforts to control COVID-19 infections. Group testing is a well-established mathematical tool, which can provide a serious and rapid improvement to this situation. In this note, we compare several well-established group testing schemes in the context of qPCR testing for COVID-19. We include example calculations, where we indicate which testing architectures yield the greatest efficiency gains in various settings. We find that for identification of individuals with COVID-19, array testing is usually the best choice, while for estimation of COVID-19 prevalence rates in the total population, Gibbs-Gower testing usually provides the most accurate estimates given a fixed and relatively small number of tests. This note is intended as a helpful handbook for labs implementing group testing methods.

We present the R package mgm for the estimation of k-order mixed graphical models (MGMs) and mixed vector autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions of MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package.

The History of Pre-Modern Medicine seminar series returns this month. The 2017–18 series – organised by a group of historians of medicine based at London universities and hosted by the Wellcome Library – will conclude with four seminars. The series… Continue reading

The last seminar in the 2017–18 History of Pre-Modern Medicine seminar series takes place on Tuesday 27 February. Speaker: Dr Dror Weil (Max Planck Institute for the History of Science, Berlin) Bodies translated: the circulation of Arabo-Persian physiological theories in late… Continue reading

National Association of Wine Retailers Release Letter Delivered to Attorneys General and Alcohol Regulatory Chiefs Concerning Unconstitutional and Unenforceable Wine Shipping Bans

(PRWeb April 15, 2020)

Read the full story at https://www.prweb.com/releases/wine_retailers_seek_alcohol_shipping_compromise_with_18_states/prweb17050617.htm

Harvested produce crops feed Florida Department of Corrections’ (FDC) more than 87,000 inmates; action saves food costs while reducing COVID-19 related supply chain impacts.

(PRWeb April 20, 2020)

Read the full story at https://www.prweb.com/releases/new_partnerships_emerge_for_covid_19_relief_dade_county_farm_bureau_teams_with_state_leaders_to_launch_farm_to_inmate_program/prweb17052045.htm

Dimitris Bertsimas, Bart Van Parys.

Source: The Annals of Statistics, Volume 48, Number 1, 300--323.

Abstract:
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes $n$ and number of regressors $p$ in the 100,000s, that is, two orders of magnitude better than the current state of the art, in seconds. The ability to solve the problem for very high dimensions allows us to observe new phase transition phenomena. Contrary to traditional complexity theory which suggests that the difficulty of a problem increases with problem size, the sparse regression problem has the property that as the number of samples $n$ increases the problem becomes easier in that the solution recovers 100% of the true signal, and our approach solves the problem extremely fast (in fact faster than Lasso), while for small number of samples $n$, our approach takes a larger amount of time to solve the problem, but importantly the optimal solution provides a statistically more relevant regressor. We argue that our exact sparse regression approach presents a superior alternative over heuristic methods available at present.

Emmanuel J. Candès, Pragya Sur.

Source: The Annals of Statistics, Volume 48, Number 1, 27--42.

Abstract:
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp “phase transition.” We introduce an explicit boundary curve $h_{mathrm{MLE}}$, parameterized by two scalars measuring the overall magnitude of the unknown sequence of regression coefficients, with the following property: in the limit of large sample sizes $n$ and number of features $p$ proportioned in such a way that $p/n ightarrow kappa $, we show that if the problem is sufficiently high dimensional in the sense that $kappa >h_{mathrm{MLE}}$, then the MLE does not exist with probability one. Conversely, if $kappa <h_{mathrm{MLE}}$, the MLE asymptotically exists with probability one.

Alessandro Rinaldo, Larry Wasserman, Max G’Sell.

Source: The Annals of Statistics, Volume 47, Number 6, 3438--3469.

Abstract:
Several new methods have been recently proposed for performing valid inference after model selection. An older method is sample splitting: use part of the data for model selection and the rest for inference. In this paper, we revisit sample splitting combined with the bootstrap (or the Normal approximation). We show that this leads to a simple, assumption-lean approach to inference and we establish results on the accuracy of the method. In fact, we find new bounds on the accuracy of the bootstrap and the Normal approximation for general nonlinear parameters with increasing dimension which we then use to assess the accuracy of regression inference. We define new parameters that measure variable importance and that can be inferred with greater accuracy than the usual regression coefficients. Finally, we elucidate an inference-prediction trade-off: splitting increases the accuracy and robustness of inference but can decrease the accuracy of the predictions.

Kyoungjae Lee, Jaeyong Lee, Lizhen Lin.

Source: The Annals of Statistics, Volume 47, Number 6, 3413--3437.

Abstract:
In this paper we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh [ Ann. Statist. (2019) 47 319–348], the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero elements in the Cholesky factor. Furthermore, our result does not require the irrepresentable condition, which is necessary for Lasso-type methods. We also derive the posterior convergence rates for precision matrices and Cholesky factors with respect to various matrix norms. The obtained posterior convergence rates are the fastest among those of the existing Bayesian approaches. In particular, we prove that our posterior convergence rates for Cholesky factors are the minimax or at least nearly minimax depending on the relative size of true sparseness for the entire dimension. The simulation study confirms that the proposed method outperforms the competing methods.

Zeng Li, Clifford Lam, Jianfeng Yao, Qiwei Yao.

Source: The Annals of Statistics, Volume 47, Number 6, 3382--3412.

Abstract:
Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in relation to the sample size $T$, the popular omnibus tests including the multivariate Hosking and Li–McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we propose a portmanteau-type test statistic which is the sum of squared singular values of the first $q$ lagged sample autocovariance matrices. It, therefore, encapsulates all the serial correlations (up to the time lag $q$) within and across all component series. Using the tools from random matrix theory and assuming both $p$ and $T$ diverge to infinity, we derive the asymptotic normality of the test statistic under both the null and a specific VMA(1) alternative hypothesis. As the actual implementation of the test requires the knowledge of three characteristic constants of the population cross-sectional covariance matrix and the value of the fourth moment of the standardized innovations, nontrivial estimations are proposed for these parameters and their integration leads to a practically usable test. Extensive simulation confirms the excellent finite-sample performance of the new test with accurate size and satisfactory power for a large range of finite $(p,T)$ combinations, therefore, ensuring wide applicability in practice. In particular, the new tests are consistently superior to the traditional Hosking and Li–McLeod tests.

Benjamin Eltzner, Stephan F. Huckemann.

Source: The Annals of Statistics, Volume 47, Number 6, 3360--3381.

Abstract:
The (CLT) central limit theorems for generalized Fréchet means (data descriptors assuming values in manifolds, such as intrinsic means, geodesics, etc.) on manifolds from the literature are only valid if a certain empirical process of Hessians of the Fréchet function converges suitably, as in the proof of the prototypical BP-CLT [ Ann. Statist. 33 (2005) 1225–1259]. This is not valid in many realistic scenarios and we provide for a new very general CLT. In particular, this includes scenarios where, in a suitable chart, the sample mean fluctuates asymptotically at a scale $n^{alpha }$ with exponents $alpha <1/2$ with a nonnormal distribution. As the BP-CLT yields only fluctuations that are, rescaled with $n^{1/2}$, asymptotically normal, just as the classical CLT for random vectors, these lower rates, somewhat loosely called smeariness, had to date been observed only on the circle. We make the concept of smeariness on manifolds precise, give an example for two-smeariness on spheres of arbitrary dimension, and show that smeariness, although “almost never” occurring, may have serious statistical implications on a continuum of sample scenarios nearby. In fact, this effect increases with dimension, striking in particular in high dimension low sample size scenarios.