Statistical model validationIn statistics, model validation is the task of evaluating whether a chosen statistical model is appropriate or not. Oftentimes in statistical inference, inferences from models that appear to fit their data may be flukes, resulting in a misunderstanding by researchers of the actual relevance of their model. To combat this, model validation is used to test whether a statistical model can hold up to permutations in the data.
Kernel principal component analysisIn the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space. Recall that conventional PCA operates on zero-centered data; that is, where is one of the multivariate observations.
Maximum likelihood estimationIn statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.
Estimation theoryEstimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
Dimensionality reductionDimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).
Induction sealingInduction sealing is the process of bonding thermoplastic materials by induction heating. This involves controlled heating an electrically conducting object (usually aluminum foil) by electromagnetic induction, through heat generated in the object by eddy currents. Induction sealing is used in many types of manufacturing. In packaging it is used for package fabrication such as forming tubes from flexible materials, attaching plastic closures to package forms, etc.
Semiparametric modelIn statistics, a semiparametric model is a statistical model that has parametric and nonparametric components. A statistical model is a parameterized family of distributions: indexed by a parameter . A parametric model is a model in which the indexing parameter is a vector in -dimensional Euclidean space, for some nonnegative integer . Thus, is finite-dimensional, and . With a nonparametric model, the set of possible values of the parameter is a subset of some space , which is not necessarily finite-dimensional.
Training, validation, and test data setsIn machine learning, a common task is the study and construction of algorithms that can learn from and make predictions on data. Such algorithms function by making data-driven predictions or decisions, through building a mathematical model from input data. These input data used to build the model are usually divided into multiple data sets. In particular, three data sets are commonly used in different stages of the creation of the model: training, validation, and test sets.
Regression validationIn statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation.
Heat sealerA heat sealer is a machine used to seal products, packaging, and other thermoplastic materials using heat. This can be with uniform thermoplastic monolayers or with materials having several layers, at least one being thermoplastic. Heat sealing can join two similar materials together or can join dissimilar materials, one of which has a thermoplastic layer. Heat sealing is the process of sealing one thermoplastic to another similar thermoplastic using heat and pressure.
