Related papers: Identifiability of Polynomial Models from First Pr…
We consider the problem of computing critical points of the restriction of a polynomial map to an algebraic variety. This is of first importance since the global minimum of such a map is reached at a critical point. Thus, these points…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. We define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is…
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
Higher-order features bring significant accuracy gains in semantic dependency parsing. However, modeling higher-order features with exact inference is NP-hard. Graph neural networks (GNNs) have been demonstrated to be an effective tool for…
We develop a method for approximating the Gr\"obner basis of the ideal of polynomials which vanish at a finite set of points, when the coordinates of the points are known with only limited precision. The method consists of a preprocessing…
Identifiability concerns finding which unknown parameters of a model can be estimated from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is…
In this study, we propose a method for extracting the hidden algebraic structures of model parameters that are uniquely determined by observed time-series data and unidentifiable state-space models, explicitly and exhaustively. State-space…
We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output…
In this paper, we give a sufficient condition for a set $\mathal G$ of polynomials to be a Gr\"obner basis with respect to a given term-order for the ideal $I$ that it generates. Our criterion depends on the linkage pattern of the ideal $I$…
Latent class models have wide applications in social and biological sciences. In many applications, pre-specified restrictions are imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners'…
Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis…
We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Two fundamental questions in the theory of Groebner bases are decision ("Is a basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is not, how do we transform it into a Groebner basis?") This paper considers the…
Labelled networks are an important class of data, naturally appearing in numerous applications in science and engineering. A typical inference goal is to determine how the vertex labels (or features) affect the network's structure. In this…
Using an off-lattice model, we fully enumerate folded conformations of polypeptide chains of up to N = 19 monomers. Structures are found to differ markedly in designability, defined as the number of sequences with that structure as a unique…
A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models:…
We give a notion of "combinatorial proximity" among strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees "geometric proximity" of the corresponding points in the Hilbert…