Breast cancer is in the most common malignant tumor in women. It accounted for 30% of new malignant tumor cases. Although the incidence of breast cancer remains high around the world, the mortality rate has been continuously reduced. This is mainly due to recent developments in molecular biology technology and improved level of comprehensive diagnosis and standard treatment. Early detection by mammography is an integral part of that. The most common breast abnormalities that may indicate breast cancer are masses and calcifications. Previous detection approaches usually obtain relatively high sensitivity but unsatisfactory specificity. We will investigate an approach that applies the discrete wavelet transform and Fourier transform to parse the images and extracts statistical features that characterize an image's content, such as the mean intensity and the skewness of the intensity. A naive Bayesian classifier uses these features to classify the images. We expect to achieve an optimal high specificity.

Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of the statistics is crucial. This choice involves a trade-off between loss of information and dimensionality reduction, and is often determined based on domain knowledge. However, handcrafting and selecting suitable statistics is a laborious task involving multiple trial-and-error steps. In this work, we introduce an active learning method for ABC statistics selection which reduces the domain expert's work considerably. By involving the experts, we are able to handle misspecified models, unlike the existing dimension reduction methods. Moreover, empirical results show better posterior estimates than with existing methods, when the simulation budget is limited.

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

As a structured prediction task, scene graph generation aims to build a visually-grounded scene graph to explicitly model objects and their relationships in an input image. Currently, the mean field variational Bayesian framework is the de facto methodology used by the existing methods, in which the unconstrained inference step is often implemented by a message passing neural network. However, such formulation fails to explore other inference strategies, and largely ignores the more general constrained optimization models. In this paper, we present a constrained structure learning method, for which an explicit constrained variational inference objective is proposed. Instead of applying the ubiquitous message-passing strategy, a generic constrained optimization method - entropic mirror descent - is utilized to solve the constrained variational inference step. We validate the proposed generic model on various popular scene graph generation benchmarks and show that it outperforms the state-of-the-art methods.

In this thesis a probabilistic framework is developed and proposed for Dynamic Object Recognition in 3D Environments. A software package is developed using C++ and Python in ROS that performs the detection and tracking task. Furthermore, a novel Gaussian Process Regression (GPR) based method is developed to detect ground points in different urban scenarios of regular, sloped and rough. The ground surface behavior is assumed to only demonstrate local input-dependent smoothness. kernel's length-scales are obtained. Bayesian inference is implemented sing \textit{Maximum a Posteriori} criterion. The log-marginal likelihood function is assumed to be a multi-task objective function, to represent a whole-frame unbiased view of the ground at each frame because adjacent segments may not have similar ground structure in an uneven scene while having shared hyper-parameter values. Simulation results shows the effectiveness of the proposed method in uneven and rough scenes which outperforms similar Gaussian process based ground segmentation methods.

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules. This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models.

We introduce a novel, probabilistic binary latent variable model to detect noisy or approximate repeats of patterns in sparse binary data. The model is based on the "Noisy-OR model" (Heckerman, 1990), used previously for disease and topic modelling. The model's capability is demonstrated by extracting structure in recordings from retinal neurons, but it can be widely applied to discover and model latent structure in noisy binary data. In the context of spiking neural data, the task is to "explain" spikes of individual neurons in terms of groups of neurons, "Cell Assemblies" (CAs), that often fire together, due to mutual interactions or other causes. The model infers sparse activity in a set of binary latent variables, each describing the activity of a cell assembly. When the latent variable of a cell assembly is active, it reduces the probabilities of neurons belonging to this assembly to be inactive. The conditional probability kernels of the latent components are learned from the data in an expectation maximization scheme, involving inference of latent states and parameter adjustments to the model. We thoroughly validate the model on synthesized spike trains constructed to statistically resemble recorded retinal responses to white noise stimulus and natural movie stimulus in data. We also apply our model to spiking responses recorded in retinal ganglion cells (RGCs) during stimulation with a movie and discuss the found structure.

Explainable artificial intelligence (XAI) aims to make learning machines less opaque, and offers researchers and practitioners various tools to reveal the decision-making strategies of neural networks. In this work, we investigate how XAI methods can be used for exploring and visualizing the diversity of feature representations learned by Bayesian neural networks (BNNs). Our goal is to provide a global understanding of BNNs by making their decision-making strategies a) visible and tangible through feature visualizations and b) quantitatively measurable with a distance measure learned by contrastive learning. Our work provides new insights into the posterior distribution in terms of human-understandable feature information with regard to the underlying decision-making strategies. Our main findings are the following: 1) global XAI methods can be applied to explain the diversity of decision-making strategies of BNN instances, 2) Monte Carlo dropout exhibits increased diversity in feature representations compared to the multimodal posterior approximation of MultiSWAG, 3) the diversity of learned feature representations highly correlates with the uncertainty estimates, and 4) the inter-mode diversity of the multimodal posterior decreases as the network width increases, while the intra-mode diversity increases. Our findings are consistent with the recent deep neural networks theory, providing additional intuitions about what the theory implies in terms of humanly understandable concepts.

The Expectation-Maximization (EM) algorithm is a way to find maximum-likelihood estimates for model parameters when the data is incomplete, or has missing data points, or has unobserved/hidden latent variables. This is an iterative way to approximate the maximum likelihood function. While maximum likelihood estimation can find the "best fit" model for a set of data, it does not work specifically well for incomplete data sets. The more complex Expectation-Maximization (EM) algorithm can find model parameters even if you have missing data. It works by selecting random values for the missing data points and using those guesses to estimate a second set of data.

Classification algorithms try to predict the class or the label of the categorical target variable. A categorical variable typically represents qualitative data that has discrete values, such as pass/fail or low/medium/high, etc. Out of the many classification algorithms, the Naïve Bayes classifier is one of the simplest classification algorithms. The Naïve Bayes classifier is often used with large text datasets among other applications. The aim of this article is to explain how the Naive Bayes algorithm works.