In this paper we contribute a novel algorithm family, which generalizes many unsupervised techniques including unnormalized and energy models, and allows us to infer different statistical modalities (e.g. data likelihood and ratio between densities) from data samples. The proposed unsupervised technique, named Probabilistic Surface Optimization (PSO), views a model as a flexible surface which can be pushed according to loss-specific virtual stochastic forces, where a dynamical equilibrium is achieved when the pointwise forces on the surface become equal. Concretely, the surface is pushed up and down at points sampled from two different distributions, with overall up and down forces becoming functions of these two distribution densities and of force intensity magnitudes defined by the loss of a particular PSO instance. Upon convergence, the force equilibrium enforces an optimized model to be equal to various statistical functions depending on the used magnitude functions. Furthermore, this dynamical-statistical equilibrium is extremely intuitive and useful, providing many implications and possible usages in probabilistic inference. We connect PSO to numerous existing statistical works which are also PSO instances, and derive new PSO-based inference methods as demonstration of PSO exceptional usability. Likewise, based on the insights coming from the virtual-force perspective we analyze PSO stability and propose new ways to improve it. Finally, we present new instances of PSO, termed PSO-LDE, for data density estimation on logarithmic scale and also provide a new NN block-diagonal architecture for increased surface flexibility, which significantly improves estimation accuracy. Both PSO-LDE and the new architecture are combined together as a new density estimation technique. We demonstrate this technique to be superior over state-of-the-art baselines.
View on arXiv