The machine-learning dataset of 51^3 ~1.3 × 10^5 density of states (DOS) of a mobile hole in the t-t'-t''-J model theoretically generated by using the self-consistent Born approximation in the three-dimensional parameter space of t′ ∈ [−0.5, 0.5], t′′ ∈ [−0.5, 0.5] and J ∈ [0.2, 1.0], with each parameter sampled on a 51-point uniform grid. The dataset is randomly partitioned into an 80/10/10 training (T), validation (V), and testing T split. Note that each DOS A(ω) was calculated on a 1201-point uniform grid of ω ∈ [−6t, 6t], then it was resampled on a 301-point uniform grid for the forward problem and on a 354-point uniform grid for the inverse problem. The dataset used in the inverse problem is limited to the parameter space of t′ ∈ [−0.5, 0], t′′ ∈ [0, 0.5] and J ∈ [0.2, 1.0]. To open the enclosed .npz files, use numpy.load() in python3. This work was supported by U.S. Department of Energy (DOE) the Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-SC0012704. This project was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internships Program (SULI). This project was supported in part by the Brookhaven National Laboratory (BNL), Condensed Matter Physics and Materials Science Division under the BNL Supplemental Undergraduate Research Program (SURP).