The following is an unsupervised machine-learning algorithm that recognizes and predicts input patterns in real-time. The algorithm is essentially a system of information-processing inspired by the cognitive functions of the mind. The system has a collection of interacting memory systems akin to the spychological concepts of short-term and long-term memory, which allows it to learn by observation and adapt based on the frequency of patterns and their relationships through time. An association value is a representation of conditional probability which is calculated between the current observation and the rest of the elements in the buffer, i.e. the previous N observations, then stored in the association matrix. Each elements current place in the buffer determines the strength of the delta applied to its association value, so more recent observation are more strongly associated with the current observations than those further in the buffer.

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.

The automation of posterior inference in Bayesian data analysis has enabled experts and nonexperts alike to use more sophisticated models, engage in faster exploratory modeling and analysis, and ensure experimental reproducibility. However, standard automated posterior inference algorithms are not tractable at the scale of massive modern datasets, and modifications to make them so are typically model-specific, require expert tuning, and can break theoretical guarantees on inferential quality. Building on the Bayesian coresets framework, this work instead takes advantage of data redundancy to shrink the dataset itself as a preprocessing step, providing fully-automated, scalable Bayesian inference with theoretical guarantees. We begin with an intuitive reformulation of Bayesian coreset construction as sparse vector sum approximation, and demonstrate that its automation and performance-based shortcomings arise from the use of the supremum norm. To address these shortcomings we develop Hilbert coresets, i.e., Bayesian coresets constructed under a norm induced by an inner-product on the log-likelihood function space. We propose two Hilbert coreset construction algorithms---one based on importance sampling, and one based on the Frank-Wolfe algorithm---along with theoretical guarantees on approximation quality as a function of coreset size. Since the exact computation of the proposed inner-products is model-specific, we automate the construction with a random finite-dimensional projection of the log-likelihood functions. The resulting automated coreset construction algorithm is simple to implement, and experiments on a variety of models with real and synthetic datasets show that it provides high-quality posterior approximations and a significant reduction in the computational cost of inference.

The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several applications, it is desirable to have a functional purely of the conditional distribution p_{Y|X,Z} rather than of the joint distribution p_{X,Y,Z}. We define the potential conditional mutual information as the conditional mutual information calculated with a modified joint distribution p_{Y|X,Z} q_{X,Z}, where q_{X,Z} is a potential distribution, fixed airport. We develop K nearest neighbor based estimators for this functional, employing importance sampling, and a coupling trick, and prove the finite k consistency of such an estimator. We demonstrate that the estimator has excellent practical performance and show an application in dynamical system inference.

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (M{\o}ller et al., 2006; Murray et al., 2006) for tackling this problem; these approaches being members of the more general class of pseudo-marginal, or exact-approximate, Monte Carlo algorithms (Andrieu and Roberts, 2009), which make use of unbiased estimates of intractable posteriors. Everitt et al. (2017) investigated the use of exact-approximate importance sampling (IS) and sequential Monte Carlo (SMC) in doubly intractable problems, but focussed only on SMC algorithms that used data-point tempering. This paper describes SMC samplers that may use alternative sequences of distributions, and describes ways in which likelihood estimates may be improved adaptively as the algorithm progresses, building on ideas from Moores et al. (2015). This approach is compared with a number of alternative algorithms for doubly intractable problems, including approximate Bayesian computation (ABC), which we show is closely related to the method of M{\o}ller et al. (2006).

We propose Bayesian hypernetworks: a framework for approximate Bayesian inference in neural networks. A Bayesian hypernetwork, $h$, is a neural network which learns to transform a simple noise distribution, $p(\epsilon) = \mathcal{N}(0,I)$, to a distribution $q(\theta) \doteq q(h(\epsilon))$ over the parameters $\theta$ of another neural network (the "primary network"). We train $q$ with variational inference, using an invertible $h$ to enable efficient estimation of the variational lower bound on the posterior $p(\theta | \mathcal{D})$ via sampling. In contrast to most methods for Bayesian deep learning, Bayesian hypernets can represent a complex multimodal approximate posterior with correlations between parameters, while enabling cheap i.i.d. sampling of $q(\theta)$. We demonstrate these qualitative advantages of Bayesian hypernets, which also achieve competitive performance on a suite of tasks that demonstrate the advantage of estimating model uncertainty, including active learning and anomaly detection.

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear functions are defined by information channels. These models have gained great popularity due to their ability to characterize complex probabilistic relationships arising in a wide variety of inference problems. The contribution of this paper is a new method for analyzing the fundamental limits of statistical inference in settings where the model is known. The validity of our method can be established in a number of settings and is conjectured to hold more generally. A key assumption made throughout is that the matrices are drawn randomly from orthogonally invariant distributions. Our method yields explicit formulas for 1) the mutual information; 2) the minimum mean-squared error (MMSE); 3) the existence and locations of certain phase-transitions with respect to the problem parameters; and 4) the stationary points for the state evolution of approximate message passing algorithms. When applied to the special case of models with multivariate Gaussian channels our method is rigorous and has close connections to free probability theory for random matrices. When applied to the general case of non-Gaussian channels, our method provides a simple alternative to the replica method from statistical physics. A key observation is that the combined effects of the individual components in the model (namely the matrices and the channels) are additive when viewed in a certain transform domain.

We begin by calculating the maximum likelihood estimates of the EVSDT parameters, separately for each participant in the data set. Before doing so, I note that this data processing is only required for manual calculation of the point estimates; the modeling methods described below take the raw data and therefore don't require this annoying step. First, we'll compute for each trial whether the participant's response was a hit, false alarm, correct rejection, or a miss. We'll do this by creating a new variable, type: Then we can simply count the numbers of these four types of trials for each participant, and put the counts on one row per participant. For a single subject, d' can be calculated as the difference of the standardized hit and false alarm rates (Stanislaw and Todorov 1999): Its inverse, \(\Phi {-1}\), converts a proportion (such as a hit rate or false alarm rate) into a z score.

Knowledge transfer between tasks can improve the performance of learned models, but requires an accurate estimate of the inter-task relationships to identify the relevant knowledge to transfer. These inter-task relationships are typically estimated based on training data for each task, which is inefficient in lifelong learning settings where the goal is to learn each consecutive task rapidly from as little data as possible. To reduce this burden, we develop a lifelong learning method based on coupled dictionary learning that utilizes high-level task descriptions to model the inter-task relationships. We show that using task descriptors improves the performance of the learned task policies, providing both theoretical justification for the benefit and empirical demonstration of the improvement across a variety of learning problems. Given only the descriptor for a new task, the lifelong learner is also able to accurately predict a model for the new task through zero-shot learning using the coupled dictionary, eliminating the need to gather training data before addressing the task.

In several domains obtaining class annotations is expensive while at the same time unlabelled data are abundant. While most semi-supervised approaches enforce restrictive assumptions on the data distribution, recent work has managed to learn semi-supervised models in a non-restrictive regime. However, so far such approaches have only been proposed for linear models. In this work, we introduce semi-supervised parameter learning for Sum-Product Networks (SPNs). SPNs are deep probabilistic models admitting inference in linear time in number of network edges. Our approach has several advantages, as it (1) allows generative and discriminative semi-supervised learning, (2) guarantees that adding unlabelled data can increase, but not degrade, the performance (safe), and (3) is computationally efficient and does not enforce restrictive assumptions on the data distribution. We show on a variety of data sets that safe semi-supervised learning with SPNs is competitive compared to state-of-the-art and can lead to a better generative and discriminative objective value than a purely supervised approach.