arXiv subjects
Publications and source records attributed to Robert R. Tucci.
We propose a Goodness of Causal Fit (GCF) measure which depends on Judea Pearl's ``do" interventions. This is different from Goodness of Fit (GF) measures, which do not use interventions. Given a set ${\cal G}$ of DAGs with the same nodes, to find a good $G\in {\cal G}$, we propose plotting $GCF(G)$ versus $GF(G)$ for all $G\in {\cal G}$, and finding a graph $G\in {\cal G}$ with a large amount of both types of goodness.
Determining a causal DAG (directed acyclic graph) for a problem under consideration, is a major roadblock when doing Judea Pearl's Causal Inference (CI) in Statistics. The same problem arises when doing CI in Artificial Intelligence (AI) and Machine Learning (ML). As with many problems in Science, we think Nature has found an effective solution to this problem. We argue that human and animal brains contain an explicit engine for doing CI, and that such an engine uses as input an atlas (i.e., collection) of causal DAGs. We propose a simple algorithm for constructing such an atlas from a library of books or videos/movies. We illustrate our method by applying it to a database of randomly generated Tic-Tac-Toe games. The software used to generate this Tic-Tac-Toe example is open source and available at GitHub.
The goal of this paper is to generalize classical d-separation and classical Belief Propagation (BP) to the quantum realm. Classical d-separation is an essential ingredient of most of Judea Pearl's work. It is crucial to all 3 rungs of what Pearl calls the 3 rungs of Causation. So having a quantum version of d-separation and BP probably implies that most of Pearl's Bayesian networks work, including his theory of causality, can be translated in a straightforward manner to the quantum realm.
We give some quantum circuits for calculating the probability $P(G|D)$ of a graph $G$ given data $D$. $G$ together with a transition probability matrix for each node of the graph, constitutes a Classical Bayesian Network, or CB net for short. Bayesian methods for calculating $P(G|D)$ have been given before (the so called structural modular and ordered modular models), but these earlier methods were designed to work on a classical computer. The goal of this paper is to "quantum computerize" those earlier methods.
In this paper, we give a quantum circuit for calculating the mean value of a function $A(x^n)\in \mathbb{C}$, where $x^n\in \{0,1\}^n$. Known classical algorithms for calculating the mean value of a structureless function $A(x^n)$ take ${\cal O}(2^n)$ steps. Our quantum algorithm is based on a Grover-like algorithm and it takes ${\cal O}(\sqrt{2^n})$ steps. Our algorithm differs significantly from previously proposed quantum algorithms for calculating the mean value of a function via Grover's algorithm.
In this paper, we give quantum circuits for calculating two closely related linear transforms that we refer to jointly as Mobius-like transforms. The first is the Mobius transform of a function $f^{-}(S^-)\in \mathbb{C}$, where $S^-\subset \{0,1,\ldots,n-1\}$. The second is a marginal of a probability distribution $P(y^n)$, where $y^n\in Bool^n$. Known classical algorithms for calculating these Mobius-like transforms take ${\cal O}(2^n)$ steps. Our quantum algorithm is based on a Grover-like algorithm and it takes ${\cal O}(\sqrt{2^n})$ steps.
In this paper, we give a quantum circuit that calculates symmetrized functions. Our algorithm applies the original Grover's algorithm or a variant thereof such as AFGA (adaptive fixed point Grover's algorithm). Our algorithm uses AFGA in conjunction with two new techniques we call "targeting two hypotheses" and "blind targeting". Suppose AFGA drives the starting state $|s\rangle$ to the target state $|t\rangle$. When targeting two hypotheses, $|t\rangle$ is a superposition $a_0|0\rangle + a_1|1\rangle$ of two orthonormal states or hypotheses $|0\rangle$ and $|1\rangle$. When targeting blindly, the value of $\langle t| s\rangle$ is not known a priori.
In this paper, we define a new information theoretic measure that we call the "uprooted information". We show that a necessary and sufficient condition for a probability $P(s|do(t))$ to be "identifiable" (in the sense of Pearl) in a graph $G$ is that its uprooted information be non-negative for all models of the graph $G$. In this paper, we also give a new algorithm for deciding, for a Bayesian net that is semi-Markovian, whether a probability $P(s|do(t))$ is identifiable, and, if it is identifiable, for expressing it without allusions to confounding variables. Our algorithm is closely based on a previous algorithm by Tian and Pearl, but seems to correct a small flaw in theirs. In this paper, we also find a {\it necessary and sufficient graphical condition} for a probability $P(s|do(t))$ to be identifiable when $t$ is a singleton set. So far, in the prior literature, it appears that only a {\it sufficient graphical condition} has been given for this. By "graphical" we mean that it is directly based on Judea Pearl's 3 rules of do-calculus.
This is a purely pedagogical paper with no new results. The goal of the paper is to give a fairly self-contained introduction to Judea Pearl's do-calculus, including proofs of his 3 rules.
We give some counterexamples to the theory of thermodynamics with feedback that has been proposed by Sagawa and Ueda. Our counterexamples are evidence that their theory, in its present form, is flawed.
We propose a new inequality that we call the conditional ageing inequality (CAIN). The CAIN is a slight generalization to non-equilibrium situations of the Second Law of thermodynamics. The goal of this paper is to study the consequences of the CAIN. We use the CAIN to discuss Maxwell demon processes (i.e., thermodynamic processes with feedback.) In particular, we apply the CAIN to four cases of the Szilard engine: for a classical or a quantum system with either one or two correlated particles. Besides proposing this new inequality that we call the CAIN, another novel feature of this paper is that we use quantum Bayesian networks for our analysis of Maxwell demon processes.
This paper follows very closely a famous paper by Csiszár and Körner about classical (non-quantum) wiretap coding. Our paper gives a self-contained and slightly novel review of some important results of the paper by Csiszár and Körner. Then we present a generalization of those results to the quantum realm, thus giving one of the first half-decent treatments of quantum wiretap coding. Like Csiszár and Körner, we too find a capacity region (i.e., the maximal achievable region of rates) characterized in terms of one-letter informations. We try to make our treatment of quantum wiretap coding as parallel a possible to our treatment of classical wiretap coding. This parallel treatment is facilitated by the use of CB nets (classical Bayesian networks) for the classical case and QB nets (quantum Bayesian networks) for the quantum one.
This paper begins with a discussion of integration over probability types (p-types). After doing that, the paper re-visits 3 mainstay problems of classical (non-quantum) Shannon Information Theory (SIT): source coding without distortion, channel coding, and source coding with distortion. The paper proves well-known, conventional results for each of these 3 problems. However, the proofs given for these results are not conventional. They are based on complex integration techniques (approximations obtained by applying the method of steepest descent to p-type integrals) instead of the usual delta & epsilon and typical sequences arguments. Another unconventional feature of this paper is that we make ample use of classical Bayesian networks (CB nets). This paper showcases some of the benefits of using CB nets to do classical SIT.
This is primarily a pedagogical paper. The paper re-visits some well-known quantum information theory inequalities. It does this from a quantum Bayesian networks perspective. The paper illustrates some of the benefits of using quantum Bayesian networks to discuss quantum SIT (Shannon Information Theory).
This paper is intended to be a pedagogical introduction to quantum Bayesian networks (QB nets), as I personally use them to represent mixed states (i.e., density matrices, and open quantum systems). A special effort is made to make contact with notions used in textbooks on quantum Shannon Information Theory (quantum SIT), such as the one by Mark Wilde (arXiv:1106.1445)
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with polynomial efficiency, certain diagonal matrix elements of an observable. This sub-algorithm is performed on a quantum computer, using quantum phase estimation and tomography. The second sub-algorithm is for sampling a probability distribution. This sub-algorithm is not polynomially efficient. It can be performed either on a classical or a quantum computer, but a quantum computer can perform it quadratically faster.
This paper introduces QOperAv v1.5, a Java application available for free. (Source code included in the distribution.) QOperAv is a "code generator" for generating quantum circuits. The quantum circuits generated by QOperAv can be used to evaluate with polynomial efficiency the average of $f(A)$ for some simple (that is, computable with polynomial efficiency) function $f$ and a Hermitian operator $A$, provided that we know how to compile $\exp(iA)$ with polynomial efficiency. QOperAv implements an algorithm described in earlier papers, that combines various standard techniques such as quantum phase estimation and quantum multiplexors.
This paper introduces Quibbs v1.3, a Java application available for free. (Source code included in the distribution.) Quibbs is a "code generator" for quantum Gibbs sampling: after the user inputs some files that specify a classical Bayesian network, Quibbs outputs a quantum circuit for performing Gibbs sampling of that Bayesian network on a quantum computer. Quibbs implements an algorithm described in earlier papers, that combines various apple pie techniques such as: an adaptive fixed-point version of Grover's algorithm, Szegedy operators, quantum phase estimation and quantum multiplexors.