Understand
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model.
- A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter.
- This work characterizes a certain strong convexity property of general exponential families, which allow their generalization ability to be quantified.
- In particular, we show how this property can be used to analyze generic exponential families under L_1 regularization.
Built on
The Theory of Probabilities
S. Bernstein · 1946
Earlier work this paper cites.
Fundamentals of Statistical Exponential Families
Lawrence D. Brown · 1986
Earlier work this paper cites.
Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity
S. Portnoy · 1988
Earlier work this paper cites.
An Introduction to Generalized Linear Models
A.J. Dobson · 1990
Earlier work this paper cites.
Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity
Subhashis Ghosal · 2000
Earlier work this paper cites.
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Then
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