Keywords: Portfolio selection, utility function, Inada condition, square-integrable, Ito-process.
Keywords: Portfolio selection, utility function, Inada condition, square-integrable, Ito-process.
Keywords: AD algorithm, evaluation trace, Dual number
Key words: Ito operator, Property of trace, Fokker-Planck equation, L2 adjoint, Hilbert space.
This note includes mean-field and structured variational families. Besides VI, mean-field and other variational family can also be used in the inference of probabilistic neural network.
Compared to MCMC, variational Inference is a faster method to approximate difficult-to-compute posterior distribution. Variational Inference is an optimization problem, while MCMC is an asymptotic method.
Metric Embedding plays an important role in unsupervised machine learning and algorithm analysis. Embedding methods are also considered as one of the most important methods in the design of approximation algorithms.
Programming is the basis for a wide range of fields. This blog summarized the sufficient conditions for strong duality. Moreover, it is a summery of Mathematical Programming lecture notes (David P. Williamson).
The parameterized function with similar training error widely diverge in the generalization performance. However, the flat minima may imply a low-complexity neural network structure. Some SGD methods have shown can converge to a flatter minima, which potentially make the solution of nonconvex optimization more robust. The first part of this note is a review of Flat minima( Hochreiter and Schmidhuber, 1997). The second part contains an introduction to Gradient Descent algorithms’ properties and visualization.
Newy-West adjustment provides a consistent estimation given autocorrelation in samples. The origin of Newy-West adjustment is closely related to Generalized Method of Moments. This blog includes the motivations, the definition and some properties of Generalized methods of Moments.
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