You can download the data set here: final_project.zip
The raw data were two-dimensional diffusion trajectories created by numerical simulation (raw data NOT included). Each trajectory represents the motion of a random walker (100,000 steps) moving in a periodic squared mesh potential. The random walk is essentially “fractional Brownian motion (fBM)”, which is a type of random walk with memory. That is, the current step size depends on the history of previous steps. A variable named “alpha” determines the amplitude of memory of fBM. Two more variables, named “mesh_size” and “penetration_rate” describe the properties of the periodic mesh potential.
To create the trajectory, first, values of “penetration_rate”, “mesh_size”, and “alpha” were randomly chosen (within a value range of interest). Given the values of the three variables, a stochastic random walk trajectory (100,000 steps) was simulated. The effects of the three variables are convoluted in the trajectory, making it difficult to estimate their individual values directly from the trajectory.
Given a simulated trajectory, we calculated its statistical characteristics and used them to construct the feature matrix (details were skipped). We used 10,000 elements as the feature for one trajectory.
We repeated the simulation for 47,500 times, giving in 47,500 trajectories. The feature matrix is 47,500 x 10,000 (see the file). The three labels “alpha”, “mesh_size”, and “penetration_rate” are 47,500 x 1 vectors (see the file).
The goal is estimate alpha, mesh_size, and penetration_rate, as precisely as possible, given the feature of a trajectory.
There are 10000 features and 3 target values for each testcase. Please try and conqure the task.