Related papers: Squared families: Searching beyond regular probabi…
We give a detailed description of the model construction procedures about our new approach to the family structure of the standard model. SM-like chiral fermion spectra, largely "derivable" from the gauge anomaly constraints, are formulated…
We review the known ways of incorporating and breaking symmetries in a renormalizable way. We summarize the various grand unified theories based on $SU_5, SO_{10}$, and $E_6$ as family enlargement groups. An $SU_5$ model with an $SU_2$…
Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
Designing expressive generative models that support exact and efficient inference is a core question in probabilistic ML. Probabilistic circuits (PCs) offer a framework where this tractability-vs-expressiveness trade-off can be analyzed…
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum…
The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…
This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the…
This paper considers regularizing a covariance matrix of $p$ variables estimated from $n$ observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
Compound distributions allow construction of a rich set of distributions. Typically they involve an intractable integral. Here we use a quadrature approximation to that integral to define the quadrature compound family. Special care is…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…
Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces…
The contribution of this work is the introduction of a multivariate circular-linear (or poly- cylindrical) distribution obtained by combining the projected and the skew-normal. We show the flexibility of our proposal, its property of…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…