Sampling (statistics)In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.
Stratified samplingIn statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population.
Simple random sampleIn statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.
Sampling frameIn statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions. Importance of the sampling frame is stressed by Jessen and Salant and Dillman. In many practical situations the frame is a matter of choice to the survey planner, and sometimes a critical one. [...] Some very worthwhile investigations are not undertaken at all because of the lack of an apparent frame; others, because of faulty frames, have ended in a disaster or in cloud of doubt.
Cluster samplingIn statistics, cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups (known as clusters) and a simple random sample of the groups is selected. The elements in each cluster are then sampled. If all elements in each sampled cluster are sampled, then this is referred to as a "one-stage" cluster sampling plan.
Machine learningMachine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.
Systematic samplingIn survey methodology, systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method. In this approach, progression through the list is treated circularly, with a return to the top once the list ends. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: where n is the sample size, and N is the population size.
Survey methodologySurvey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods for improving the number and accuracy of responses to surveys. Survey methodology targets instruments or procedures that ask one or more questions that may or may not be answered.
Diffusion modelIn machine learning, diffusion models, also known as diffusion probabilistic models or score-based generative models, are a class of latent variable models. They are Markov chains trained using variational inference. The goal of diffusion models is to learn the latent structure of a dataset by modeling the way in which data points diffuse through the latent space. In computer vision, this means that a neural network is trained to denoise images blurred with Gaussian noise by learning to reverse the diffusion process.
Nonparametric statisticsNonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance).
Sampling biasIn statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Constrained optimizationIn mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.
Statistical inferenceStatistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.
Bootstrapping (statistics)Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimand (such as its variance) by measuring those properties when sampling from an approximating distribution.
Deep learningDeep learning is part of a broader family of machine learning methods, which is based on artificial neural networks with representation learning. The adjective "deep" in deep learning refers to the use of multiple layers in the network. Methods used can be either supervised, semi-supervised or unsupervised.
TensorFlowTensorFlow is a free and open-source software library for machine learning and artificial intelligence. It can be used across a range of tasks but has a particular focus on training and inference of deep neural networks. TensorFlow was developed by the Google Brain team for internal Google use in research and production. The initial version was released under the Apache License 2.0 in 2015. Google released the updated version of TensorFlow, named TensorFlow 2.0, in September 2019.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Unsupervised learningUnsupervised learning, is paradigm in machine learning where, in contrast to supervised learning and semi-supervised learning, algorithms learn patterns exclusively from unlabeled data. Neural network tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised (see Venn diagram); however, the separation is very hazy. For example, object recognition favors supervised learning but unsupervised learning can also cluster objects into groups.
Group method of data handlingGroup method of data handling (GMDH) is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully automatic structural and parametric optimization of models. GMDH is used in such fields as data mining, knowledge discovery, prediction, complex systems modeling, optimization and pattern recognition. GMDH algorithms are characterized by inductive procedure that performs sorting-out of gradually complicated polynomial models and selecting the best solution by means of the external criterion.
