Related papers: Oracle computability of conditional expectations o…
Under a general structural equation framework for causal inference, we provide a definition of the causal effect of a variable X on another variable Y, and propose an approach to estimate this causal effect via the use of instrumental…
We show that if $M$ is a full factor and $N \subset M$ is a co-amenable subfactor with expectation, then $N$ is also full. This answers a question of Popa from 1986. We also generalize a theorem of Tomatsu by showing that if $M$ is a full…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We consider lambda-Y-calculus as a non-interpreted functional programming language: the result of the execution of a program is its normal form that can be seen as the tree of calls to built-in operations. Weak monadic second-order logic…
This paper presents some of the basic properties of conditioned observables in finite-dimensional quantum mechanics. We begin by defining the sequential product of quantum effects and use this to define the sequential product of two…
We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, Markov chain Monte Carlo methods can be used for performing exact tests,…
Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and…
A canonical desideratum for prediction problems is that performance guarantees should hold not just on average over the population, but also for meaningful subpopulations within the overall population. But what constitutes a meaningful…
In a noncontextual hidden variable model of quantum theory, hidden variables determine the outcomes of every measurement in a manner that is independent of how the measurement is implemented. Using a generalization of this notion to…
We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there exists sufficient random variables X and Y, such…
It is shown explicitly that the correlation functions of Conformal Field Theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of $\W_\infty$-algebra. This algebra is constructed…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
In this paper, some ?-classes of weighted conditional expectation type operators, such as A-class, ?-A-class and quasi-?-A classes on L2(?) are investigated. Also, the spectrum, point spectrum and spectral radius of these operators are…
Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This…
We show that the standard computational pipeline of probabilistic programming systems (PPSs) can be inefficient for estimating expectations and introduce the concept of expectation programming to address this. In expectation programming,…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
We show that there exists an oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal…
A systematic algorithm for building integrating factors of the form mu(x,y') or mu(y,y') for non-linear second order ODEs is presented. When such an integrating factor exists, the algorithm determines it without solving any differential…
We investigate causal computations taking sequences of inputs to sequences of outputs where the $n$th output depends on the first $n$ inputs only. We model these in category theory via a construction taking a Cartesian category $C$ to…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…