Exponentially concave functions

Author: wstx

August undefined, 2024

WebSep 1, 2024 · A real-valued function φ on an open convex domain D in R n is said to be exponentially concave if exp φ is a concave function on D. For usual practices in convex analysis, we will assume our functions to take the value − ∞ outside their domains, thereby extending them to the entire space. WebThe function is said to be concave (resp. strictly concave) if (multiplied by −1) is convex (resp. strictly convex). Alternative naming. The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or …

Logarithmic divergences from optimal transport and Rényi

WebJan 18, 2014 · Remark 1. As indicated in Theorems 1 and 2, the excess risk for both batch learning and online learning is reduced at the rate of O(dlogn/n), which is consistent with the regret bound for online optimizing the exponentially concave loss functions [ 1]. We note that the linear dependence on d is in general unavoidable. WebIn this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized by an exponentially concave … men\u0027s health ultimate guy

Exponential Functions Examples & Transformations - Study.com

WebA function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper, we showed that gradient maps of exponentially concave functions provide solutions to a … WebMar 29, 2014 · Here is an example. Consider the density of two exponential random variables as \begin{align*} f_1(x) &=\lambda_1 \exp(-\lambda_1x) \\ f_2(x) &=\lambda_2 \exp ... WebMay 19, 2016 · We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better … how much to neuter a cat in ireland

Example of sum of log-concave is not always log-concave

WebNov 3, 2024 · Exponentially convex (concave) functions can be considered as a significant extension of the convex functions and have important applications in information theory, big data analysis,... WebMar 30, 2024 · Using the definition of the exponential type convex function for k=1, we have f ( m ) \leq ( e-1 ) f (m)\Longrightarrow0\leq (e-2)f (m)\Longrightarrow f (m)\geq0 . . We discuss some connections between the class of exponential type convex functions and … men\\u0027s health usaWebApr 11, 2024 · The most significant difference between an exponential graph and a quadratic graph is the nature of the function itself. An exponential function always increases or decreases, depending on the sign of the base number, whereas a quadratic function can either increase or decrease, depending on whether it is concave up or … how much to neuter a cat in bc

"WebMay 19, 2016 · We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient … " - Exponentially concave functions

Exponentially concave functions

Loss functions for classification - Wikipedia

WebThe logarithm f(x) = logxis concave on the interval 0 <1, and the exponential f(x) = ex is convex everywhere. 3. f(x) is convex i f(x) is concave. 4. You can combine basic convex functions to build more complicated convex functions. If f(x) is convex, then g(x) = cf(x) … http://earthmath.kennesaw.edu/main_site/RSI_studies/MenuTopics/Exponential%20Functions.htm

Did you know?

WebSep 30, 2024 · A function is called the exponentially m -concave function f, if − f is an exponentially m -convex function. It is obvious that theses two concepts are equivalent. These equivalent formulations have been used to discuss various aspects of the exponentially convex functions. WebA function is called the exponentially general concave function f, if fis exponen-tially general convex function. De nition 2.9. A function Fis said to be exponentially general a ne convex function with respect to an arbitrary non-negative function g;if

WebWhile simple models from the exponential family with concave like-lihoods like regression or lasso (Tibshirani, 1996) still play an important role in big-data applications ... optimization because when the optimization procedure2 has found a maximum of a concave likelihood function, it has clearly reached the global maximum if only one exists. ...

http://www.ifp.illinois.edu/~angelia/L3_convfunc.pdf WebThe exponential function is a mathematical function denoted by () = ⁡ or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a …

WebFeb 16, 2024 · Types of Exponential Functions. There are 2 types of exponential functions namely: Exponential Decay Function; Exponential Growth Function; Exponential Growth Function: In exponential growth as the name suggests a quantity …

WebMar 3, 2024 · An exponential function is a mathematical function that is commonly used in real-world applications. It is primarily used to compute investments, model populations, and so on. This article will teach you about the formulas, rules, properties, graphs, … men\\u0027s health urbanathlon san franciscoWebFor example, a quadratic function ’(x) = ax2 + bx+ c is convex if a 0, and is concave if a 0. Unfortunately, the de nitions above are not su ciently general, since they require ’to be twice di erentiable. Instead, we will use the following de nitions: De nition: Convex and Concave Functions Let 1 a men\u0027s health urbanathlon san franciscoWebAug 14, 2024 · The exponentially convex functions have important applications in information theory, big data analysis, machine learning and statistic. See, for example, [1,2,3,4,5,6,13,14, 20,... men\u0027s health usa april 2019Web1. Log-concave densities / distributions: de nitions Suppose that a density f can be written as f(x) f’(x) = exp(’(x)) = exp( ( ’(x))) where ’is concave (and ’is convex). The class of all densities f on R, or on Rd, of this form is called the class of log-concave densities, Plog … men\u0027s health usaWebpractical methods for establishing convexity of a function 1. verify deﬁnition (often simpliﬁed by restricting to a line) 2. for twice diﬀerentiable functions, show ∇2f(x) 0 3. show that f is obtained from simple convex functions by operations that preserve convexity • nonnegative weighted sum • composition with aﬃne function men\u0027s health ultimate male reviewWebExponential families: the log partition function Consider an exponential family distribution with sufﬁcient statistic s(X) and natural parameter (and no base factor in X alone). We can write its probability or density function as p (Xj ) = exp Ts X)( where ( ) is thelog partition … men\u0027s health usa january 2016WebExponentially concave functions have been applied to several recent results related to optimal transport. For example, in [ 13] it was used to prove the equivalence of the entropic curvature-dimension condition and Bochner’s inequality. men\u0027s health urination problems