The Frame Problem (FP) is a puzzle in philosophy of mind and epistemology, articulated by the Stanford Encyclopedia of Philosophy as follows: "How do we account for our apparent ability to make decisions on the basis only of what is relevant to an ongoing situation without having explicitly to consider all that is not relevant?" In this work, we focus on the causal variant of the FP, the Causal Frame Problem (CFP). Assuming that a reasoner's mental causal model can be (implicitly) represented by a causal Bayes net, we first introduce a notion called Potential Level (PL). PL, in essence, encodes the relative position of a node with respect to its neighbors in a causal Bayes net. Drawing on the psychological literature on causal judgment, we substantiate the claim that PL may bear on how time is encoded in the mind. Using PL, we propose an inference framework, called the PL-based Inference Framework (PLIF), which permits a boundedly-rational approach to the CFP to be formally articulated at Marr's algorithmic level of analysis. We show that our proposed framework, PLIF, is consistent with a wide range of findings in causal judgment literature, and that PL and PLIF make a number of predictions, some of which are already supported by existing findings.

The ability to learn tasks in a sequential fashion is crucial to the development of artificial intelligence. Neural networks are not, in general, capable of this and it has been widely thought that catastrophic forgetting is an inevitable feature of connectionist models. We show that it is possible to overcome this limitation and train networks that can maintain expertise on tasks which they have not experienced for a long time. Our approach remembers old tasks by selectively slowing down learning on the weights important for those tasks. We demonstrate our approach is scalable and effective by solving a set of classification tasks based on the MNIST hand written digit dataset and by learning several Atari 2600 games sequentially.

We consider the problem of segmenting a large population of customers into non-overlapping groups with similar preferences, using diverse preference observations such as purchases, ratings, clicks, etc. over subsets of items. We focus on the setting where the universe of items is large (ranging from thousands to millions) and unstructured (lacking well-defined attributes) and each customer provides observations for only a few items. These data characteristics limit the applicability of existing techniques in marketing and machine learning. To overcome these limitations, we propose a model-based projection technique, which transforms the diverse set of observations into a more comparable scale and deals with missing data by projecting the transformed data onto a low-dimensional space. We then cluster the projected data to obtain the customer segments. Theoretically, we derive precise necessary and sufficient conditions that guarantee asymptotic recovery of the true customer segments. Empirically, we demonstrate the speed and performance of our method in two real-world case studies: (a) 84% improvement in the accuracy of new movie recommendations on the MovieLens data set and (b) 6% improvement in the performance of similar item recommendations algorithm on an offline dataset at eBay. We show that our method outperforms standard latent-class and demographic-based techniques.

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel methods can be extended to probability measures. It can be viewed as a generalization of the original "feature map" common to support vector machines (SVMs) and other kernel methods. While initially closely associated with the latter, it has meanwhile found application in fields ranging from kernel machines and probabilistic modeling to statistical inference, causal discovery, and deep learning. The goal of this survey is to give a comprehensive review of existing work and recent advances in this research area, and to discuss the most challenging issues and open problems that could lead to new research directions. The survey begins with a brief introduction to the RKHS and positive definite kernels which forms the backbone of this survey, followed by a thorough discussion of the Hilbert space embedding of marginal distributions, theoretical guarantees, and a review of its applications. The embedding of distributions enables us to apply RKHS methods to probability measures which prompts a wide range of applications such as kernel two-sample testing, independent testing, and learning on distributional data. Next, we discuss the Hilbert space embedding for conditional distributions, give theoretical insights, and review some applications. The conditional mean embedding enables us to perform sum, product, and Bayes' rules---which are ubiquitous in graphical model, probabilistic inference, and reinforcement learning---in a non-parametric way. We then discuss relationships between this framework and other related areas. Lastly, we give some suggestions on future research directions.

Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node to change over continuous time. Three settings are developed for learning non-stationary continuous time Bayesian networks from data: known transition times, known number of epochs and unknown number of epochs. A score function for each setting is derived and the corresponding learning algorithm is developed. A set of numerical experiments on synthetic data is used to compare the effectiveness of non-stationary continuous time Bayesian networks to that of non-stationary dynamic Bayesian networks.

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in a variational Bayesian framework where the goal is to provide a good approximation to the posterior distribution in order to compute posterior mean estimates. Moreover, a majorization technique is employed to circumvent the difficulties raised by the intricate forms of the non-Gaussian likelihood and of the prior density. We demonstrate the potential of the proposed approach through comparisons with state-of-the-art techniques that are specifically tailored to signal recovery in the presence of mixed Poisson-Gaussian noise. Results show that the proposed approach is efficient and achieves performance comparable with other methods where the regularization parameter is manually tuned from the ground truth.

All the regression theory developed by statisticians over the last 200 years (related to the general linear model) is useless. Regression can be performed as accurately without statistical models, including the computation of confidence intervals (for estimates, predicted values or regression parameters). The non-statistical approach is also more robust than theory described in all statistics textbooks and taught in all statistical courses. It does not require Map-Reduce when data is really big, nor any matrix inversion, maximum likelihood estimation, or mathematical optimization (Newton algorithm). It is indeed incredibly simple, robust, easy to interpret, and easy to code (no statistical libraries required).

A few months ago, Autonomy founder and CEO Mike Lynch sold his company to HP for £7.1 billion. Back in 2000, when he had just become Britain's first software billionaire, Lynch gave an interview in which he talked about perception and explained how he built his company. It was based, he said, on the ideas of a little-known 18th-century clergyman called Thomas Bayes. That was my introduction to Thomas Bayes, whose ideas have been used to solve many intractable problems, a number of which Sharon Bertsch McGrayne studies in depth in The Theory That Would Not Die. In the last ten years, Bayes has become famous, and few working in the field of probability theory, computer intelligence or mathematics can have failed to have come into contact with his rule.

We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an efficient MCMC inference algorithm that advances recent work on augmentation schemes for inference in negative binomial models. Finally, we demonstrate the model's inductive bias using a variety of real-world data sets, showing that it exhibits superior predictive performance over other models and infers highly interpretable latent structure.

Here is an excellent ILP reference, somewhat older but publicly available. The most recent issue of SIGKDD Explorations is a special issue devoted to multi-relational data mining.