Peripheral vision plays an important role in human vision, directing where and when tomake saccades. Although human behavior in the periphery is well-predicted by pyramid-based texture models, these approaches rely on hand-picked image statistics that are stillinsufficient to capture a wide variety of textures. To develop a more principled approach tostatistic selection for texture-based models of peripheral vision, we develop a self-supervisedmachine learning model to determine what set of statistics are most important for repre-senting texture. Our model, which we call StatTexNet, uses contrastive learning to take alarge set of statistics and compress them to a smaller set that best represents texture fami-lies. We validate our method using depleted texture images where the constituent statisticsare already known. We then use StatTexNet to determine the most and least importantstatistics for natural (non-depleted) texture images using weight interpretability metrics,finding these to be consistent with previous psychophysical studies. Finally, we demonstratethat textures are most effectively synthesized with the statistics identified as important;we see noticeable deterioration when excluding the most important statistics, but minimaleffects when excluding least important. Overall, we develop a machine learning method ofselecting statistics that can be used to create better peripheral vision models. With thesebetter models, we can more effectively understand the effects of peripheral vision in humangaze.