Generalized Maximum Entropy Estimation
Authors: Tobias Sutter, David Sutter, Peyman Mohajerin Esfahani, John Lygeros
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We further demonstrate how the presented scheme can be used for approximating the chemical master equation through the zero-information moment closure method, and for an approximate dynamic programming approach in the context of constrained Markov decision processes with uncountable state and action spaces. (Abstract) The simulation results, Figure 2, show the time trajectory for the average and the second moment of the number of M molecules in the reversible dimerization model (26), as calculated for the zero information closure (25) using Algorithm 1, for a second-order closure as well as a third-order closure. To solve the ODE (25) we use an explicit Runge-Kutta (4,5) formula (ode45) built into MATLAB. The results are compared to the average of 106 SSA Wilkinson (2006) trajectories. It can be seen how increasing the order of the closure method improves the approximation accuracy. (Section 6) Numerical Simulation. For a given set of model parameters...we consider four different scenarios...For each scenario we run Algorithm 2 and plot the value of the resulting approximation J(k) n,ζ as a function of the number of iterations in Figure 3. (Section 7.2) |
| Researcher Affiliation | Academia | Tobias Sutter EMAIL Risk Analytics and Optimization Chair EPFL, Switzerland; David Sutter EMAIL Institute for Theoretical Physics ETH Zurich, Switzerland; Peyman Mohajerin Esfahani EMAIL Delft Center for Systems and Control TU Delft, The Netherlands; John Lygeros EMAIL Department of Electrical Engineering and Information Technology ETH Zurich, Switzerland |
| Pseudocode | Yes | Algorithm 1: Optimal scheme for smooth & strongly convex optimization Choose w0 = y0 RM and η R2 >0 For k 0 do Step 1: Set yk+1 = wk + 1 L(η) Fη(wk) Step 2: Compute wk+1 = yk+1 + L(η)+ η2 (yk+1 yk) [*The stopping criterion is explained in Remark 7]; Algorithm 2: Approximate dynamic programming scheme Input: n, k N, ζ, θ > 0, and w(0) Rn+1 such that w(0) 2 θ For 0 ℓ k do Step 1: Define r(ℓ) := ζ 4n(e Tn y ζ(w(ℓ))) Step 2: Let z(ℓ) := T Pℓ j=0 j+1 2 r(j), 0 and β(ℓ) = T r(ℓ), w(ℓ) Step 3: Set w(ℓ+1) = 2 ℓ+3z(ℓ) + ℓ+1 Output: J(k) n,ζ := c, ˆyζ + θ Tnˆyζ e 2 with ˆyζ := Pk j=0 2(j+1) (k+1)(k+2) y ζ(w(j)) |
| Open Source Code | No | The paper does not provide explicit statements about open-sourcing the code, a repository link, or mention of code in supplementary materials. |
| Open Datasets | No | The paper does not provide concrete access information for a publicly available or open dataset. Example 1 uses a synthetic setup with given moments. Section 6 and 7.2 describe models and simulation parameters rather than external datasets. |
| Dataset Splits | No | The paper does not discuss standard datasets with train/test/validation splits, as the examples provided involve synthetic data generation or simulations based on models. |
| Hardware Specification | Yes | Simulations were run with Matlab on a laptop with a 2.2 GHz Intel Core i7 processor. (Footnote 3) and 1000 iterations of Algorithm 2 took around 5.5 hours with Matlab on a laptop with a 2.2 GHz Intel Core i7 processor. (Footnote 6). |
| Software Dependencies | No | Simulations were run with Matlab on a laptop with a 2.2 GHz Intel Core i7 processor. (Footnote 3). The paper does not provide specific version numbers for Matlab or other key software components. |
| Experiment Setup | Yes | We consider two simulations for two different uncertainty sets (namely, u = 0.01 and u = 0.005)...A Slater point is constructed using the method described in Remark 8, where r = 5 is enough for the problem (17) to be feasible, leading to the constant C = 0.0288. (Section 3, Example 1) Reversible dimerization system (26) with reaction constants K = k2/k1...The initial conditions are M0 = 10 and D0 = 0 and the regularization term κ = 0.01. (Figure 2 caption) Algorithm 1: η1 = η2 = 10^-3, 1500 iterations; Algorithm 2: ζ = 10^-1.5, θ = 3, n = 10, Fourier basis u2i-1(s) = C / (2iπ) cos(2iπs/C) and u2i(s) = C / (2iπ) sin(2iπs/C) for i = 1, . . . , n (Section 7.2, Numerical Simulation) |