Using Stochastics

Harish Bhat

Harish Bhat, associate professor of mathematics, likes to tackle difficult problems and find solutions that help people, especially if he can use novel approaches in math or computer science. “I got into stochastics and machine learning because I enjoy solving real-world problems,” he said, “and finding solutions often involves using models and algorithms from these areas.”

He recently joined the U’s Math Department after teaching for a decade at the University of California, Merced. “When I joined UC Merced,” he noted, “it was still the newest campus in the UC system, so it felt a bit like a startup—there was always plenty to do besides the usual teaching and research duties.” In addition to teaching, Bhat served on faculty hiring committees and developed curricula for undergraduate and graduate students.

Algorithms and Forecasting

Initially he got into stochastics (an area concerned with random probabilities) and machine learning through the subprime loan financial crisis of 2008. He and another graduate student saw this focus as a way to develop a more accurate pricing model, and they began using machine learning that relied on using short-term memory models instead of the usual Black-Scholes-Merton model that uses long-term price variation. “We developed and used a large database of historical option prices to show that our model could outperform competing models, such as Black-Scholes,” said Bhat. Data collection played a huge role in both the development

and testing of their model. Following this, Bhat worked with Silicon Valley Bank to build models to forecast startup earnings; to evaluate and determine the price for common and preferred shares issued by startups with venture capital funding; and to predict the potential bankruptcy rates of startups.

Today Bhat teaches and does research in two areas. He works with public health researchers to build machine-learning models that can predict (and help prevent) suicides within a target group. This is of interest because suicide rates have increased over the past decade in Utah as well as in other western states. “We need to figure out the reasons for the increase,” said Bhat, “and find ways to help those at risk. But we also need better tools to help mental health professionals, educators, counselors, and families determine who is at risk. Both machine learning and deep learning show promise in helping us build stateof-the-art prediction algorithms.”

Bhat also develops algorithms that can automatically infer motion equations from time series data. For example, if there were enough videos of apples falling from trees, could an algorithm automatically discover the differential equation that governs the position of the apple as a function of time? Bhat sees applying this technique to complex systems, such as cognitive science models; quantum chemistry models for many-body systems in time-dependent potentials; and powergrid models that incorporate renewable energy sources such as wind and solar power.

Raised in San Jose, Calif., Bhat attended Harvard University and graduated with a degree in mathematics. While there, he took classes in computer science, philosophy, and literature. He was a weekly deejay on WHRB-FM, the latenight on-campus indie/punk rock radio station.

He regularly attended the Brattle Theatre and the Harvard Film Archive, soaking up the work of classic filmmakers such as Satyajit Ray, Akira Kurosawa, and François Truffaut.

At Caltech, he was part of a small, interdisciplinary Ph.D. program called “Control and Dynamical Systems.” He became interested in the mathematics of compressible fluid flow and shock waves, and his thesis explored new Lagrangian and Hamiltonian methods to smooth out Euler equations for a compressible fluid. “I have fond memories of my years at Caltech because I worked with some incredible people,” he said.

As a newcomer to Utah, Bhat is interested in learning about Salt Lake City and the state. One thing he’s already discovered is the local coffee scene. “I love that there are so many places to get an espresso on campus, including, but not limited to: Two Creek, Brio, and Coffee Lab,” he said. “I’ve also visited places around the city—there is clearly a burgeoning coffee culture here, and I’m grateful!” Bhat is married and has two young kids. In his leisure hours, he spends time with his family, discovers local musicians, and enjoys hiking and skiing.

As he continues his research on suicide prevention, the goal is to improve the machine-learning models and training methods. His work on the equations of motion is progressing, but he admits there is still much to learn. “I’m really excited to be at the U. There’s great potential to collaborate, and I expect to find a number of researchers whose interests overlap with mine,” he said. “Together, I’m hoping we can make great strides.”