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Questions tagged [stochastic-approximation]

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An optimal stochastic problem and Monte-carlo

Assume we are in a Brownian filtration where I denote $W$ the Brownian motion. My problem is to numerically compute $$ \min_X E (\int^1_0 X^2_tdt),\ \ \ \ (*) $$ where $X$ is adapted to the filtration ...
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Posterior convergence in expectation vs probability

Let's assume that we are doing approximate Bayesian inference and compute the convergence of our posterior estimate to the true value of the parameter using Wasserstein distance. Why posterior ...
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26 views

Age-structured SIR/SEIR binomial chain model

To make ODE models stochastic, a binomial distribution can be used to model the number of new infections, e.g. SIR/SIS [1] and SEIR [2]. The derivation of these models makes sense, as they assume ...
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180 views

How to solve / fit a geometric brownian motion process in Python?

For example, the below code simulates Geometric Brownian Motion (GBM) process, which satisfies the following stochastic differential equation: The code is a condensed version of the code in this ...
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Is it possible to combine SPSA and Adam?

In SGD algorithms such as Adam you generally make a bad estimate of the gradient of the loss function and take that gradient to move the parameters in the desired direction. Gradient free methods ...
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Comparing estimators for stochastic approximation

Given a stochastic approximation setting $f(\theta^*) = \max\limits_\theta\mathbb{E}[F(\theta,X)]$ where our goal is to maximize $f(\theta)$ with respect to $\theta$ using a series of samples of the ...
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Log Euler simulation scheme for Cox–Ingersoll–Ross model

https://en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model In this article the Cox–Ingersoll–Ross is given. I want to design a simulation scheme for this process. A continuous SDE can be ...
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196 views

Difference between Stochastic Approximation (SA) and Stochastic Gradient Descent (SGD)

I understand the intended use cases for both stochastic approximation algorithms like SPSA or FDSA, and for SGD algorithms like Adam. SPSA is intended for noisy objective functions, and Adam for ...
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1answer
96 views

Best estimate for Stochastic difference equation

On the subject of Stochastic differential equations. If we consider the difference equation $$\Delta x(t_n) = x(t_n) \Delta t + f(t_n) \Delta t$$ where we consider $f(t_n) \Delta t$, the driving term ...
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SGD shows the same convergence behaviour as batch gradient descent when using adaptive learning rate?

SGD shows the same convergence behaviour as batch gradient descent when using adaptive learning rate ? I dont understand why he claimed that. I couldnt find any reference about it in any paper. ...
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1answer
107 views

Simulation of Secretary problem: optimal pool size given k=2?

Question: Is it incorrect to think there is a "sweet spot" where more samples slightly decreases the likelihood of a "Best pick" in the Secretary Problem? Details: The "Secretary Problem" from "...
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1answer
479 views

Confusion about Robbins-Monro algorithm in Bishop PRML

This is basically how Robbins-Monro is presented in chapter 2.3 of Bishop's PRML book (from his slides): In the general update equation, $$ \theta^{(N)} = \theta^{(N-1)} - \alpha_{N-1}z(θ^{(N-1)}) $$ ...
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1answer
2k views

Stochastic gradient descent: why randomise training set

I'm given a dataset of 200 million training examples. The stochastic gradient descent method requires me to sample these randomly, to avoid it gets 'stuck'. First and for all, I don't see how it ...
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1answer
65 views

Can you perform stochastic learning followed by batch learning in neural networks?

I'm trying to teach myself about neural networks. I've been reading through the "Efficient BackProp" paper that's highly sited and it's brought me this question; Since stochastic learning converges ...
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53 views

Optimizing a function available only through (monte-carlo) stochastic approximation

I am working on a problem where I want to estimate the maximum of a density that I can, in practice, evaluate (pointwisely) using a Monte-Carlo approach (because of intractable integrals). Obviously, ...
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Which methods do people use to understand queueing networks?

Queueing networks can be analyzed through analytic results (in some cases), approximation methods or simulation (discrete-event simulation, system dynamics). Analytic solutions do not exist in general....
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1answer
2k views

How do I compare the the sampling distribution of the minimum of a distribution by sample sizes

I saw this question (link) but when I read it, I see that it has a fixed "N" so I thought it was asking about for a finite sample size. When I read the answer that it was suggested to be a duplicate ...
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1answer
25 views

what does analyzing an algorithm in the stochastic setting mean?

Does stochastic setting for a data mean that the distribution of the data is fixed, and data points are getting generated i.i.d from that distribution? If not, what does it usually mean? Thank you
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1answer
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Is it a good idea to use $\eta = \arg \max( L(y, f(x) )$ to choose the step size for stochastic gradient descent (SGD)?

I wanted to have a good (as optimal as possible) automatic way of choosing the step size for minimizing the generalization error $\mathbb{E}_{ (x,y) \sim p_{x,y} }[L(y, f(x))]$, where $L$ is the loss ...
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144 views

Apply gradient descent on expected valued cost function

I want to use gradient descent algorithm to minimize the Kurtosis of the error function. So, I need to calculate the gradient of the cost function $J$. Below $\boldsymbol{w}$ and $\boldsymbol{x}$ are ...
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What are some major theories on picking the right number for the sample window size in time series analysis?

for example the number of samples to run the moving average, or the number of samples for sequential hypothesis testing. Or if there is a control scheme going on what is the best time window for an ...
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594 views

Stochastic Differential Equations - A Few General Questions

I just have a few questions about stochastic differential equations. I generally did a lot of pure math but signed up for a course on probability models and stochastic differential equations because I ...
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2answers
373 views

Frequency distribution of Chinese Restaurant Process?

Set-up I was simulating the Generalized Chinese Restaurant Process as shown on the wikipedia page [link] with a discount, $\alpha$, and concentration parameter $\theta$ For $n=5$ total customers ...
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2answers
2k views

Is Markov chain based sampling the “best” for Monte Carlo sampling? Are there alternative schemes available?

Markov Chain Monte Carlo is a method based on Markov chains that allows us to obtain samples (in a Monte Carlo setting) from non-standard distributions from which we cannot draw samples directly. My ...
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1answer
129 views

100 m sprint world record times - lower bound

Can we find the lowest attainable bound for the 100 m sprint times, i.e. the quickest it can be run ever, using the past data? So every now and again the record gets broken and we can map the new ...
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106 views

Rootfinding in the presence of one-sided noise

I'm faced with a practical problem of solving for a 1-D function which has noise, so find myself in the territory of stochastic approximation (and I am well out of my comfort zone here!). I know ...