Unsupervised learning in generative models of occlusion

The ability to identify the objects in a visual scene is a central task in every-day life. So far, no computer algorithm has achieved to match the capabilities of the human brain to learn and recognize image components. These can be objects, object parts, or low-level features like edges, depending on the brain area considered or the model used. The reasons for this lie in the high complexity of both our brain architecture and visual data. The pronounced parallelization and plasticity of neural structure together with the great amount of neurons only allow for models and simulations of small subregions of the brain. In addition, visual scenes are of a highly variable nature: Di erent numbers of objects, lighting conditions, background, space and rotation invariance, deformations, and especially occlusions lead to the fact that two scenes are never completely alike. To model the way in which lower visual brain areas learn and build representations of the world, several statistical approaches have been established. These models and the corresponding learning algorithms use the assumption that the gray values of object components combine by a pixel-wise sum. Concerning visual data, this is a vast mathematical simpli cation, which deviates from the true physics because only the opaque object closest to the observer determines the pixel value in an image. Especially when describing colored RGB-value pictures, this linear approximation become inapplicable. Another assumption used by many of these models is that components are superimposed according to continuous weight coe cients, which deviates from the spike-encoded neural property to either contribute to an activity pattern or not. Despite these simpli cations, such models extract edges, or Gabor wavelets, from visual scene snippets. These components correspond to the representations that neurons in lower visual brain areas use to encode visual scenes. In my work, I investigate models that use more realistic assumptions for the combination of visual components on the one hand and for neuronal properties on the other. All projects were carried out in close collaboration with others. My contributions will be mentioned explicitly at the beginning of each chapter. With the Binary Sparse Coding model we still follow the linearity assumption but we exchange the continuous with binary (0,1) coe cients. In addition to modelling neuronal systems more closely, this allows for the application of a the approximation scheme Expectation Truncation (ET) which gives us the opportunity to scale model parameters and data dimensions to a range which is infeasible with other approaches in the literature. Using e cient unsupervised learning, we are able to learn all model parameters including data noise and sparseness of contributing components. When learning from visual scenes with this model and approximation scheme, we reliably extract a representation of Gabor lters which ts with the representation of parts of visual cortex as well as the learned elds of older standard methods. In direct comparison it is notable that we extract, in addition, globular elds, i.e. round components which have been observed in primary visual cortex but are, by other approaches, only obtained under speci cally chosen conditions. In addition to a better computational e ciency and to learning more model parameters than is common in the literature, we also obtain results which t physiological data of the brain more closely. Exchanging the linear approximation with a realistic combination of model components leads to higher computational complexity as well as to analytical issues in the form of non-di erentiable functions which need to be approximated by an appropriate choice of a di erentiable function in order to develop a successful learning algorithm. By applying ET to a model where the linear combination has been replaced by a pixelwise max operation we can directly compare the extracted components for both approaches. Using a classi er, we detect for the non-linear model a constant and higher percentage of globular elds which ts physiological data much more closely than the linear approaches. Additionally, the edges chosen by the non-linear model to code a given data point are much more aligned to the stimulus edges than those of a linear model. We thus conclude that visual areas in the cortex do not follow a linear approximation but explicitly account for occlusions. However, the max combination denotes an approximation for the combination of visual components as well. With Occlusive Components Analysis we thus introduce a model which more accurately re ects the physics of visual object combination. Such models typically represent higher visual area modelling where neurons do not code edges but rather complete objects or object parts. The introduction of this complex combination rule leads to non-di erentiable functions as pointed out above as well as to numerical instabilities and a computational complexity of the algorithm which renders it inapplicable to pictures of common sizes and containing a typical number of objects. The main contribution of this work lies in solutions for how to overcome these issues by applying the ET scheme. We show that we are able to develop update rules