Approximate Decentralized Bayesian Inference

This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines its set of received local posteriors. The key insight in this work is that, for many Bayesian models, approximate inference schemes destroy symmetry and dependencies in the model that are crucial to the correct application of Bayes' rule when combining the local posteriors. The proposed method addresses this issue by including an additional optimization step in the combination procedure that accounts for these broken dependencies. Experiments on synthetic and real data demonstrate that the decentralized method provides advantages in computational performance and predictive test likelihood over previous batch and distributed methods.Comment: This paper was presented at UAI 2014. Please use the following BibTeX citation: @inproceedings{Campbell14_UAI, Author = {Trevor Campbell and Jonathan P. How}, Title = {Approximate Decentralized Bayesian Inference}, Booktitle = {Uncertainty in Artificial Intelligence (UAI)}, Year = {2014}

No. 16: The State of Food Insecurity in Msunduzi Municipality, South Africa

There is plenty of food in Msunduzi, in South Africa’s KwaZulu-Natal province, but the urban poor regularly go hungry. This study of Msunduzi’s food security situation formed part of AFSUN’s baseline survey of eleven Southern African cities. The survey results show that the urban poor in Msunduzi are significantly worse off than their counterparts in Cape Town and Johannesburg. A third of the households reported that they sometimes or often have no food to eat of any kind. Household size did not make a great deal of difference to levels of insecurity but female-headed households are more food insecure than male-headed households. Msunduzi is a classic case study of a city whose food supply system is dominated by modern supermarket supply chains. The informal food economy is relatively small, urban agriculture is not especially significant in the city and informal rural-urban food transfers are lower than in many other cities surveyed. In this respect, Msunduzi offers the other cities a picture of their own future. Supermarket expansion is occurring at an extremely rapid rate throughout southern Africa, tying urban spaces and populations into global, regional and national supply chains. While supermarkets offer greater variety and fresher produce than many other outlets, they clearly do not meet the needs of the poor

Truncated Random Measures

Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM representations---series representations and superposition representations---within which we organize both novel and existing sequential representations that can be used for simulation and posterior inference. These two classes and their constituent representations subsume existing ones that have previously been developed in an ad hoc manner for specific processes. Since a complete infinite-dimensional CRM cannot be used explicitly for computation, sequential representations are often truncated for tractability. We provide truncation error analyses for each type of sequential representation, as well as their normalized versions, thereby generalizing and improving upon existing truncation error bounds in the literature. We analyze the computational complexity of the sequential representations, which in conjunction with our error bounds allows us to directly compare representations and discuss their relative efficiency. We include numerous applications of our theoretical results to commonly-used (normalized) CRMs, demonstrating that our results enable a straightforward representation and analysis of CRMs that has not previously been available in a Bayesian nonparametric context.Comment: To appear in Bernoulli; 58 pages, 3 figure

Ariadne: An interface to support collaborative database browsing:Technical Report CSEG/3/1995

This paper outlines issues in the learning of information searching skills. We report on our observations of the learning of browsing skills and the subsequent iterative development and testing of the Ariadne system – intended to investigate and support the collaborative learning of search skills. A key part of this support is a mechanism for recording an interaction history and providing students with a visualisation of that history that they can reflect and comment upon

Forward stagewise regression and the monotone lasso

We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the least angle regression algorithm, with a small modification, solves the lasso regression problem. Here we give an analogous result for incremental forward stagewise regression, showing that it solves a version of the lasso problem that enforces monotonicity. One consequence of this is as follows: while lasso makes optimal progress in terms of reducing the residual sum-of-squares per unit increase in $L_1$-norm of the coefficient $\beta$, forward stage-wise is optimal per unit $L_1$ arc-length traveled along the coefficient path. We also study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the lasso and forward stagewise procedures in a simulation study involving a large number of correlated predictors.Comment: Published at http://dx.doi.org/10.1214/07-EJS004 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Virtue Theoretic Solution to the Problem of Moral Luck

At the beginning of his famous paper “Moral Luck,” Thomas Nagel notes that it is intuitively plausible that people cannot be morally assessed for what is beyond their control. He then argues that most, if not all, of what people do is beyond their control. Thus, Nagel concludes that individuals must deny that people cannot be morally assessed for what is beyond their control, alter the way they think about morality, or abandon the belief that moral assessment is possible. I contend that one’s best option is to alter the way one thinks about morality and therefore draw from the work of Michael J. Zimmerman to construct and defend a counterfactual theory of moral assessment which looks not only at the kind of person one is and the kinds of actions one performs but also at the kind of person one would be and the kinds of actions one would perform in certain counterfactual circumstances. In closing, I explain why one who accepts my counterfactual theory of moral assessment has reason to prefer virtue ethical theories of morality to their consequentialist and deontological counterparts