Arthur C. Clarke famously stated that "any sufficiently advanced technology is indistinguishable from magic." No current technology embodies this statement more than neural networks and deep learning. And like any good magic it not only dazzles and inspires but also puts fear into people's hearts. One known property of artificial neural networks (ANNs) is that they are universal function approximators. This means that any mathematical function can be represented by a neural network.

Bayesian probability theory states that it's possible to predict with surprising accuracy the likelihood of something happening (or not happening) in a transparent and analytically defensible way. A Bayesian inference network, or model, captures every element of a problem and calculates possible outcomes mathematically. The harder the problem, the better it works--at least in theory. In reality, a typical approach is to gather a roomful of PhDs and spend a lot of time and money building a Bayesian network. Then, with even greater effort and more man-hours, the Bayesian network is turned into software by a roomful of coders.

Since in the former case, the numerator involves expectation wrt to q and q2, hence it supports mixtures.

The ability to accurately forecast and control inpatient census, and thereby workloads, is a critical and longstanding problem in hospital management. Majority of current literature focuses on optimal scheduling of inpatients, but largely ignores the process of accurate estimation of the trajectory of patients throughout the treatment and recovery process. The result is that current scheduling models are optimizing based on inaccurate input data. We developed a Clustering and Scheduling Integrated (CSI) approach to capture patient flows through a network of hospital services. CSI functions by clustering patients into groups based on similarity of trajectory using a novel Semi-Markov model (SMM)-based clustering scheme proposed in this paper, as opposed to clustering by admit type or condition as in previous literature. The methodology is validated by simulation and then applied to real patient data from a partner hospital where we see it outperforms current methods. Further, we demonstrate that extant optimization methods achieve significantly better results on key hospital performance measures under CSI, compared with traditional estimation approaches, increasing elective admissions by 97% and utilization by 22% compared to 30% and 8% using traditional estimation techniques. From a theoretical standpoint, the SMM-clustering is a novel approach applicable to any temporal-spatial stochastic data that is prevalent in many industries and application areas.

How is Bayes' Theorem used in artificial intelligence and machine learning? Is there any good book that you can recommend? As an high school student I will be writing an essay about it, and I want to use the best sources that I can find. I need a source that explains bayes' theorem, its general use and how it is used in AI or ML?

In coming years residential consumers will face real-time electricity tariffs with energy prices varying day to day, and effective energy saving will require automation - a recommender system, which learns consumer's preferences from her actions. A consumer chooses a scenario of home appliance use to balance her comfort level and the energy bill. We propose a Bayesian learning algorithm to estimate the comfort level function from the history of appliance use. In numeric experiments with datasets generated from a simulation model of a consumer interacting with small home appliances the algorithm outperforms popular regression analysis tools. Our approach can be extended to control an air heating and conditioning system, which is responsible for up to half of a household's energy bill.

Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o} update still remains, after more than 50 years, a valuable baseline which is difficult to improve upon, though in its original form it is a heuristic and not a proper statistical "model". Mathematically, the \'{E}l\H{o} rating system is very closely related to the Bradley-Terry models, which are usually used in an explanatory fashion rather than in a predictive supervised or on-line learning setting. Exploiting this close link between these two model classes and some newly observed similarities, we propose a new supervised learning framework with close similarities to logistic regression, low-rank matrix completion and neural networks. Building on it, we formulate a class of structured log-odds models, unifying the desirable properties found in the above: supervised probabilistic prediction of scores and wins/draws/losses, batch/epoch and on-line learning, as well as the possibility to incorporate features in the prediction, without having to sacrifice simplicity, parsimony of the Bradley-Terry models, or computational efficiency of \'{E}l\H{o}'s original approach. We validate the structured log-odds modelling approach in synthetic experiments and English Premier League outcomes, where the added expressivity yields the best predictions reported in the state-of-art, close to the quality of contemporary betting odds.

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.