Improved Iterative Scaling Research Articles

Maximum-Entropy-Model-Enabled Complexity Reduction Algorithm in Modern Video Coding Standards

Symmetry considerations play a key role in modern science, and any differentiable symmetry of the action of a physical system has a corresponding conservation law. Symmetry may be regarded as reduction of Entropy. This work focuses on reducing the computational complexity of modern video coding standards by using the maximum entropy principle. The high computational complexity of the coding unit (CU) size decision in modern video coding standards is a critical challenge for real-time applications. This problem is solved in a novel approach considering CU termination, skip, and normal decisions as three-class making problems. The maximum entropy model (MEM) is formulated to the CU size decision problem, which can optimize the conditional entropy; the improved iterative scaling (IIS) algorithm is used to solve this optimization problem. The classification features consist of the spatio-temporal information of the CU, including the rate–distortion (RD) cost, coded block flag (CBF), and depth. For the case analysis, the proposed method is based on High Efficiency Video Coding (H.265/HEVC) standards. The experimental results demonstrate that the proposed method can reduce the computational complexity of the H.265/HEVC encoder significantly. Compared with the H.265/HEVC reference model, the proposed method can reduce the average encoding time by 53.27% and 56.36% under low delay and random access configurations, while Bjontegaard Delta Bit Rates (BD-BRs) are 0.72% and 0.93% on average.

Iterative Scaling in Curved Exponential Families

AbstractThe paper describes a generalized iterative proportional fitting procedure that can be used for maximum likelihood estimation in a special class of the general log‐linear model. The models in this class, called relational, apply to multivariate discrete sample spaces that do not necessarily have a Cartesian product structure and may not contain an overall effect. When applied to the cell probabilities, the models without the overall effect are curved exponential families and the values of the sufficient statistics are reproduced by the MLE only up to a constant of proportionality. The paper shows that Iterative Proportional Fitting, Generalized Iterative Scaling, and Improved Iterative Scaling fail to work for such models. The algorithm proposed here is based on iterated Bregman projections. As a by‐product, estimates of the multiplicative parameters are also obtained. An implementation of the algorithm is available as an R‐package.

An Extension of Iterative Scaling for Decision and Data Aggregation in Ensemble Classification

Improved iterative scaling (IIS) is an algorithm for learning maximum entropy (ME) joint and conditional probability models, consistent with specified constraints, that has found great utility in natural language processing and related applications. In most IIS work on classification, discrete-valued "feature functions" are considered, depending on the data observations and class label, with constraints measured based on frequency counts, taken over hard (0---1) training set instances. Here, we consider the case where the training (and test) set consist of instances of probability mass functions on the features, rather than hard feature values. IIS extends in a natural way for this case. This has applications (1) to ME classification on mixed discrete-continuous feature spaces and (2) to ME aggregation of soft classifier decisions in ensemble classification. Moreover, we combine these methods, yielding a method, with proved learning convergence, that jointly performs (soft) decision-level and feature-level fusion in making ensemble decisions. We demonstrate favorable comparisons against standard Adaboost.M1, input-dependent boosting, and other supervised combining methods, on data sets from the UC Irvine Machine Learning repository.