Related papers: In- and Equivariance for Optimal Designs in Genera…
Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…
Hierarchical random effect models are used for different purposes in clinical research and other areas. In general, the main focus is on population parameters related to the expected treatment effects or group differences among all units of…
The diffusion probabilistic generative models are widely used to generate high-quality data. Though they can synthetic data that does not exist in the training set, the rationale behind such generalization is still unexplored. In this…
Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of…
Under the Neyman causal model, it is well-known that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to…
We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group $\mathcal{G}$ that acts discretely on the input and output of a standard neural network layer $\phi_{W}: \Re^{M} \to…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
We propose a variance-penalized formulation of Bayesian optimal experimental design for nonlinear models that augments the classical expected utility criterion with a penalty on utility variability, yielding a mean--variance objective that…
We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…
The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint…
Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an…
In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…
Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as…
In this paper, the tools provided by the theory of Optimal Experimental Design are applied to a nonlinear calibration model. This is motivated by the need of estimating radiation doses using radiochromic films for radiotherapy purposes. The…
Machine learning models rely on various assumptions to attain high accuracy. One of the preliminary assumptions of these models is the independent and identical distribution, which suggests that the train and test data are sampled from the…
This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…
Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…