The present work investigates a generalization of previous contributions in the analysis of data frames. Our contributions can be summarized as follows.

An estimated 610,000 people in the US died from cancer last year. That's almost the same amount of people who perished in the country's four-year civil war. At least two million more people were diagnosed with some form of cancer in 2024, a figure that's climbed in recent years. Early detection remains one of the single biggest factors that determine whether or not someone ultimately survives cancer and, luckily, advances in medical treatment can help. Researchers and medical scientists believe artificial intelligence models could play a key role in that early detection process.

While some surveys show that people prefer to talk to a human as opposed to a chatbot, whether they're shopping online or dealing with a customer service issue, that hasn't dissuaded companies from adopting them. A 2019 Salesforce report found that 53% of service organizations expected to use chatbots within 18 months. According to Statista, the size of the global chatbot market could surpass $1.25 billion by 2025, a steep climb from $190 million in 2016. A customer's satisfaction -- or lack thereof -- with a chatbot ultimately depends on the scenario and the capabilities of the chatbot in question. Obviously, a chatbot that fails to answer basic questions will lead to frustration.

Many applications of machine learning involve the analysis of large data frames -- matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples -- with missing values. Low-rank models, as studied by Udell et al. (2016), are popular in this framework for tasks such as visualization, clustering and missing value imputation. Yet, available methods with statistical guarantees and efficient optimization do not allow explicit modeling of main additive effects such as row and column, or covariate effects. In this paper, we introduce a low-rank interaction and sparse additive effects (LORIS) model which combines matrix regression on a dictionary and low-rank design, to estimate main effects and interactions simultaneously. We provide statistical guarantees in the form of upper bounds on the estimation error of both components. Then, we introduce a mixed coordinate gradient descent (MCGD) method which provably converges sub-linearly to an optimal solution and is computationally efficient for large scale data sets. We show on simulated and survey data that the method has a clear advantage over current practices.

Many applications of machine learning involve the analysis of large data frames -- matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples -- with missing values. Low-rank models, as studied by Udell et al. (2016), are popular in this framework for tasks such as visualization, clustering and missing value imputation. Yet, available methods with statistical guarantees and efficient optimization do not allow explicit modeling of main additive effects such as row and column, or covariate effects. In this paper, we introduce a low-rank interaction and sparse additive effects (LORIS) model which combines matrix regression on a dictionary and low-rank design, to estimate main effects and interactions simultaneously. We provide statistical guarantees in the form of upper bounds on the estimation error of both components. Then, we introduce a mixed coordinate gradient descent (MCGD) method which provably converges sub-linearly to an optimal solution and is computationally efficient for large scale data sets. We show on simulated and survey data that the method has a clear advantage over current practices.

Thanks to digital tools equipped with artificial intelligence, we're (theoretically) better than we used to be. Devices and apps track our workouts, our sleep patterns, our periods, our sexual encounters. We give these digital spies access to any intimate part of our lives, whatever they demand, because we assume having more data will allow us to see where we're failing, and to make improvements accordingly. But, if you had data on how the kinds of conversations you had with other people, would it make you a better person? Can AI actually teach us to communicate better -- you know, with other humans? Startup founder Nancy Lublin thinks the answer is yes.

Crisis Text Line, a nonprofit that offers emotional support through text messaging, has spent four years connecting people in extreme emotional duress with online counselors. Now its founder is creating a startup called Loris.ai to help companies teach employees how to communicate. "There are a lot of companies right now that are fearful of having hard conversations," says Nancy Lublin, the founder of both Crisis Text Line and Loris.ai. "Managers are nervous having a one-on-one meeting with a direct report of a different gender, and that holds women back. People worrying about inclusion worry they'll get it wrong, and that holds people back."