Graphics processing units (GPUs) are of increasing interest because they offer massive parallelism for high-throughput computing. While GPUs promise high peak performance, their challenge is a less-familiar programming model with more complex and irregular performance trade-offs than traditional CPUs or CMPs. In particular, modest changes in software or hardware characteristics can lead to large or unpredictable changes in performance. In response to these challenges, our work proposes, evaluates, and offers usage examples of Stargazer 1, an automated GPU performance exploration framework based on stepwise regression modeling. Stargazer sparsely and randomly samples parameter values from a full GPU design space and simulates these designs. Then, our automated stepwise algorithm uses these sampled simulations to build a performance estimator that identifies the most significant architectural parameters and their interactions. The result is an application-specific performance model which can accurately predict program runtime for any point in the design space. Because very few initial performance samples are required relative to the extremely large design space, our method can drastically reduce simulation time in GPU studies. For example, we used Stargazer to explore a design space of nearly 1 million possibilities by sampling only 300 designs. For 11 GPU applications, we were able to estimate their runtime with less than 1.1% average error. In addition, we demonstrate several usage scenarios of Stargazer.