scholarly journals A generalized Fourier transform by means of change of variables within multilinear approximation

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mathilde Chevreuil ◽  
Myriam Slama
Keyword(s):  
Learning Algorithm ◽  
Statistical Error ◽  
Reynolds Numbers ◽  
Low Complexity ◽  
Low Rank ◽  
Trigonometric Polynomials ◽  
Change Of Variables ◽  
Functional Representation ◽  
Random Samples ◽  
Selection Of

AbstractThe paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation and adapted parametrizations for the approximation. Such representation enables to approximate multivariate functions with few eventually random samples. The new parametrization is determined automatically with a greedy procedure, and a low rank format is used for the approximation associated with each new parametrization. A supervised learning algorithm is used for the approximation of a function of multiple random variables in tree-based tensor format, here the particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed for the selection of the underlying tensor bases and the ranks for the Tensor-Train format. The method is applied for the estimation of the wall pressure for a flow over a cylinder for a range of low to medium Reynolds numbers for which we observe two flow regimes: a laminar flow with periodic vortex shedding and a laminar boundary layer with a turbulent wake (sub-critic regime). The automatic re-parametrization enables here to take into account the specific periodic feature of the pressure.

scholarly journals Non-random sampling and association tests on realized returns and risk proxies

2021 ◽  
Author(s):  
Frank Ecker ◽  
Jennifer Francis ◽  
Per Olsson ◽  
Katherine Schipper
Keyword(s):  
Random Sampling ◽  
Reference Sample ◽  
Positive Association ◽  
Cost Of Equity ◽  
Association Tests ◽  
Random Samples ◽  
Distribution Matching ◽  
Matched Samples ◽  
Data Requirements ◽  
Selection Of

AbstractThis paper investigates how data requirements often encountered in archival accounting research can produce a data-restricted sample that is a non-random selection of observations from the reference sample to which the researcher wishes to generalize results. We illustrate the effects of non-random sampling on results of association tests in a setting with data on one variable of interest for all observations and frequently-missing data on another variable of interest. We develop and validate a resampling approach that uses only observations from the data-restricted sample to construct distribution-matched samples that approximate randomly-drawn samples from the reference sample. Our simulation tests provide evidence that distribution-matched samples yield generalizable results. We demonstrate the effects of non-random sampling in tests of the association between realized returns and five implied cost of equity metrics. In this setting, the reference sample has full information on realized returns, while on average only 16% of reference sample observations have data on cost of equity metrics. Consistent with prior research (e.g., Easton and Monahan The Accounting Review 80, 501–538, 2005), analysis using the unadjusted (non-random) cost of equity sample reveals weak or negative associations between realized returns and cost of equity metrics. In contrast, using distribution-matched samples, we find reliable evidence of the theoretically-predicted positive association. We also conceptually and empirically compare distribution-matching with multiple imputation and selection models, two other approaches to dealing with non-random samples.

scholarly journals Monotonic Functions Method and Its Application to Staging of Patients with Prostate Cancer According to Pretreatment Data

2021 ◽  
Vol 11 (9) ◽  
pp. 3836
Author(s):  
Valeri Gitis ◽  
Alexander Derendyaev ◽  
Konstantin Petrov ◽  
Eugene Yurkov ◽  
Sergey Pirogov ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Learning Algorithm ◽  
Binary Classification ◽  
Preoperative Staging ◽  
Threshold Value ◽  
Logical Function ◽  
Adequate Treatment ◽  
Monotonic Functions ◽  
Selection Of

Prostate cancer is the second most frequent malignancy (after lung cancer). Preoperative staging of PCa is the basis for the selection of adequate treatment tactics. In particular, an urgent problem is the classification of indolent and aggressive forms of PCa in patients with the initial stages of the tumor process. To solve this problem, we propose to use a new binary classification machine-learning method. The proposed method of monotonic functions uses a model in which the disease’s form is determined by the severity of the patient’s condition. It is assumed that the patient’s condition is the easier, the less the deviation of the indicators from the normal values inherent in healthy people. This assumption means that the severity (form) of the disease can be represented by monotonic functions from the values of the deviation of the patient’s indicators beyond the normal range. The method is used to solve the problem of classifying patients with indolent and aggressive forms of prostate cancer according to pretreatment data. The learning algorithm is nonparametric. At the same time, it allows an explanation of the classification results in the form of a logical function. To do this, you should indicate to the algorithm either the threshold value of the probability of successful classification of patients with an indolent form of PCa, or the threshold value of the probability of misclassification of patients with an aggressive form of PCa disease. The examples of logical rules given in the article show that they are quite simple and can be easily interpreted in terms of preoperative indicators of the form of the disease.

A Low-Complexity Three-Stage Estimator for Low-Rank mmWave Channels

2021 ◽  
pp. 1-1
Author(s):  
Khawaja Fahad Masood ◽  
Rui Hu ◽  
Jun Tong ◽  
Jiangtao Xi ◽  
Qinghua Guo ◽  
...  
Keyword(s):  
Low Complexity ◽  
Low Rank

scholarly journals Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Biometrika ◽  
2020 ◽  
Author(s):  
S Na ◽  
M Kolar ◽  
O Koyejo
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Graphical Model ◽  
Brain Connectivity ◽  
Statistical Error ◽  
Real Data ◽  
Low Rank ◽  
Conditional Dependence ◽  
Gradient Descent Algorithm ◽  
The Difference

Abstract Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

Least Square Regression with lp-Coefficient Regularization

2010 ◽  
Vol 22 (12) ◽  
pp. 3221-3235 ◽  
Author(s):  
Hongzhi Tong ◽  
Di-Rong Chen ◽  
Fenghong Yang
Keyword(s):  
Error Analysis ◽  
Learning Algorithm ◽  
Learning Rate ◽  
Least Square ◽  
Explicit Learning ◽  
Regularization Term ◽  
Least Square Regression ◽  
Primary Focus ◽  
Selection Of

The selection of the penalty functional is critical for the performance of a regularized learning algorithm, and thus it deserves special attention. In this article, we present a least square regression algorithm based on lp-coefficient regularization. Comparing with the classical regularized least square regression, the new algorithm is different in the regularization term. Our primary focus is on the error analysis of the algorithm. An explicit learning rate is derived under some ordinary assumptions.

scholarly journals Does Tail Label Help for Large-Scale Multi-Label Learning

2018 ◽  
Author(s):  
Tong Wei ◽  
Yu-Feng Li
Keyword(s):  
Large Scale ◽  
Performance Metrics ◽  
Learning Algorithm ◽  
Predictive Performance ◽  
Low Complexity ◽  
Tail Distribution ◽  
Prediction Time ◽  
Unseen Data ◽  
Model Size ◽  
Fast Prediction

Large-scale multi-label learning annotates relevant labels for unseen data from a huge number of candidate labels. It is well known that in large-scale multi-label learning, labels exhibit a long tail distribution in which a significant fraction of labels are tail labels. Nonetheless, how tail labels make impact on the performance metrics in large-scale multi-label learning was not explicitly quantified. In this paper, we disclose that whatever labels are randomly missing or misclassified, tail labels impact much less than common labels in terms of commonly used performance metrics (Top-$k$ precision and nDCG@$k$). With the observation above, we develop a low-complexity large-scale multi-label learning algorithm with the goal of facilitating fast prediction and compact models by trimming tail labels adaptively. Experiments clearly verify that both the prediction time and the model size are significantly reduced without sacrificing much predictive performance for state-of-the-art approaches.

Computational Study of Grooved Microchannel Enhancements

2008 ◽  
Author(s):  
Stephen A. Solovitz
Keyword(s):  
Thermal Management ◽  
Computational Study ◽  
Internal Flow ◽  
Reynolds Numbers ◽  
Thermal Dissipation ◽  
Two Dimensional ◽  
Macro Scale ◽  
Flow Heat ◽  
Alternate Solution ◽  
Selection Of

As electronics devices continue to increase in thermal dissipation, novel methods will be necessary for effective thermal management. Many macro-scale enhancement techniques have been developed to improve internal flow heat transfer, with a dimple feature being particularly promising due to its enhanced mixing with potentially little pressure penalty. However, because dimples may be difficult to fashion in microchannels, two-dimensional grooves are considered here as a similar alternate solution. Computational fluid dynamics methods are used to analyze the flow and thermal performance for a groove-enhanced microchannel, and the effectiveness is determined for a range of feature depths, diameters, and flow Reynolds numbers. By producing local impingement and flow redevelopment downstream of the groove, thermal enhancements on the order of 70% were achieved with pressure increases of only 30%. Further optimization of this concept should allow the selection of an appropriate application geometry, which can be studied experimentally to validate the concept.

scholarly journals Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems

Sensors ◽  
2019 ◽  
Vol 19 (15) ◽  
pp. 3368
Author(s):  
Rui Hu ◽  
Jun Tong ◽  
Jiangtao Xi ◽  
Qinghua Guo ◽  
Yanguang Yu
Keyword(s):  
Covariance Matrix ◽  
Communication Systems ◽  
Low Complexity ◽  
Low Rank ◽  
Covariance Matrix Estimation ◽  
Hardware Complexity ◽  
Matrix Estimation ◽  
Planar Arrays ◽  
Rank Matrix ◽  
Low Rank Matrix

Hybrid massive MIMO structures with lower hardware complexity and power consumption have been considered as potential candidates for millimeter wave (mmWave) communications. Channel covariance information can be used for designing transmitter precoders, receiver combiners, channel estimators, etc. However, hybrid structures allow only a lower-dimensional signal to be observed, which adds difficulties for channel covariance matrix estimation. In this paper, we formulate the channel covariance estimation as a structured low-rank matrix sensing problem via Kronecker product expansion and use a low-complexity algorithm to solve this problem. Numerical results with uniform linear arrays (ULA) and uniform squared planar arrays (USPA) are provided to demonstrate the effectiveness of our proposed method.

scholarly journals Transfer Incremental Learning Using Data Augmentation

2018 ◽  
Vol 8 (12) ◽  
pp. 2512 ◽  
Author(s):  
Ghouthi Boukli Hacene ◽  
Vincent Gripon ◽  
Nicolas Farrugia ◽  
Matthieu Arzel ◽  
Michel Jezequel
Keyword(s):  
Incremental Learning ◽  
Deep Neural Networks ◽  
Data Augmentation ◽  
State Of The Art ◽  
Low Complexity ◽  
Computational Power ◽  
Learning Problem ◽  
Learning Techniques ◽  
Using Data ◽  
Selection Of

Deep learning-based methods have reached state of the art performances, relying on a large quantity of available data and computational power. Such methods still remain highly inappropriate when facing a major open machine learning problem, which consists of learning incrementally new classes and examples over time. Combining the outstanding performances of Deep Neural Networks (DNNs) with the flexibility of incremental learning techniques is a promising venue of research. In this contribution, we introduce Transfer Incremental Learning using Data Augmentation (TILDA). TILDA is based on pre-trained DNNs as feature extractors, robust selection of feature vectors in subspaces using a nearest-class-mean based technique, majority votes and data augmentation at both the training and the prediction stages. Experiments on challenging vision datasets demonstrate the ability of the proposed method for low complexity incremental learning, while achieving significantly better accuracy than existing incremental counterparts.

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