Probabilistic models are popular tools for data analysis and machine learning. Many of the standard inference algorithms are, however, computationally heavy and can only be used for small-scale applications with limited amount of data. This seminar is about efficient alternatives that can be used also for big data applications. The focus is in recent theoretical advances in efficient inference applicable to a variety of models, including topics such as stochastic variational inference, stochastic gradient Monte Carlo methods, and other accelerated gradient algorithms.