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Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

In recent years we see a rapidly growing line of research which shows learnability of various models via common neural network algorithms. Yet, besides a very few outliers, these results show learnability of models that can be learned using…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

We analyze the problem of network identifiability with nonlinear functions associated with the edges. We consider a static model for the output of each node and by assuming a perfect identification of the function associated with the…

A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…

Epistemic uncertainty is often viewed as a reducible uncertainty that vanishes with increasing data. This perspective implicitly assumes parameter identifiability and equates epistemic uncertainty with predictive variability. In…

We leverage probabilistic models of neural representations to investigate how residual networks fit classes. To this end, we estimate class-conditional density models for representations learned by deep ResNets. We then use these models to…

Neural networks have a number of shortcomings. Amongst the severest ones is the sensitivity to distribution shifts which allows models to be easily fooled into wrong predictions by small perturbations to inputs that are often imperceivable…

Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…

Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…

We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…

Neural networks have become a popular tool in predictive modelling, more commonly associated with machine learning and artificial intelligence than with statistics. Generalised Additive Models (GAMs) are flexible non-linear statistical…

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

It is widely believed that deep neural networks contain layer specialization, wherein neural networks extract hierarchical features representing edges and patterns in shallow layers and complete objects in deeper layers. Unlike common…

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values…

In this paper, we show that feedforward and recurrent neural networks exhibit an outer product derivative structure but that convolutional neural networks do not. This structure makes it possible to use higher-order information without…

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this…

Explainability is an essential reason limiting the application of neural networks in many vital fields. Although neuro-symbolic AI hopes to enhance the overall explainability by leveraging the transparency of symbolic learning, the results…