Related papers: Algorithmic statistics revisited
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
Curriculum learning is a training strategy that sorts the training examples by some measure of their difficulty and gradually exposes them to the learner to improve the network performance. Motivated by our insights from implicit curriculum…
In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…
Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by…
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…
Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…
Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…
Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because…
The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness and discuss how a discrepancy between uniqueness class and…
Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…
Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…