Developed back in the 50s by Rosenblatt and colleagues, this extremely simple algorithm can be viewed as the foundation for some of the most successful classifiers today, including suport vector machines and logistic regression, solved using stochastic gradient descent. The convergence proof for the Perceptron algorithm is one of the most elegant pieces of math I've seen in ML. Most useful: Boosting, especially boosted decision trees. This intuitive approach allows you to build highly accurate ML models, by combining many simple ones. Boosting is one of the most practical methods in ML, it's widely used in industry, can handle a wide variety of data types, and can be implemented at scale.

Since about 100 years ago, to learn the intrinsic structure of data, many representation learning approaches have been proposed, including both linear ones and nonlinear ones, supervised ones and unsupervised ones. Particularly, deep architectures are widely applied for representation learning in recent years, and have delivered top results in many tasks, such as image classification, object detection and speech recognition. In this paper, we review the development of data representation learning methods. Specifically, we investigate both traditional feature learning algorithms and state-of-the-art deep learning models. The history of data representation learning is introduced, while available resources (e.g. online course, tutorial and book information) and toolboxes are provided. Finally, we conclude this paper with remarks and some interesting research directions on data representation learning.

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

Monte Carlo methods, such as MCMC and SMC, have been central to the application of Bayesian statistics to real-world problems (Robert and Casella, 2011; McGrayne, 2011). These established Monte Carlo methods are based upon simulating discrete-time Markov processes. For example MCMC algorithms simulate a discrete-time Markov chain constructed to have a target distribution of interest, the posterior distribution in Bayesian inference, as its stationary distribution. Whilst SMC methods involve propagating and re-weighting particles so that a final set of weighted particles approximate a target distribution. The propagation step here also involves simulating from a discrete-time Markov chain. 1 In the past few years there have been exciting developments in MCMC and SMC methods based on continuoustime versions of these Monte Carlo methods. For example, continuous-time MCMC algorithms have been proposed (Peters and de With, 2012; Bouchard-Côté et al., 2015; Bierkens and Roberts, 2015; Bierkens et al., 2016) that involve simulating a continuous-time Markov process that has been designed to have a target distribution of interest as its stationary distribution. These continuous-time MCMC algorithms were originally motivated as they are examples of nonreversible Markov processes. There is substantial evidence that nonreversible MCMC algorithms will be more efficient than standard MCMC algorithms that are reversible (Neal, 1998; Diaconis et al., 2000; Neal, 2004; Bierkens, 2015), and there is empirical evidence that these continuous-time MCMC algorithms are more efficient than their discrete-time counterparts (see e.g.

Deep belief nets are one of the most exciting recent developments in artificial intelligence. The structure of these elegant models is much closer to that of human brains than traditional neural networks; they have a'thought process' that is capable of learning abstract concepts built from simpler primitives. A typical deep belief net can learn to recognize complex patterns by optimizing millions of parameters, yet this model can still be resistant to overfitting. This book presents the essential building blocks of the most common forms of deep belief nets. At each step the text provides intuitive motivation, a summary of the most important equations relevant to the topic, and concludes with highly commented code for threaded computation on modern CPUs as well as massive parallel processing on computers with CUDA-capable video display cards.

Recurrent neural networks (RNNs) are powerful and effective for processing sequential data. However, RNNs are usually considered "black box" models whose internal structure and learned parameters are not interpretable. In this paper, we propose an interpretable RNN based on the sequential iterative soft-thresholding algorithm (SISTA) for solving the sequential sparse recovery problem, which models a sequence of correlated observations with a sequence of sparse latent vectors. The architecture of the resulting SISTA-RNN is implicitly defined by the computational structure of SISTA, which results in a novel stacked RNN architecture. Furthermore, the weights of the SISTA-RNN are perfectly interpretable as the parameters of a principled statistical model, which in this case include a sparsifying dictionary, iterative step size, and regularization parameters. In addition, on a particular sequential compressive sensing task, the SISTA-RNN trains faster and achieves better performance than conventional state-of-the-art black box RNNs, including long-short term memory (LSTM) RNNs.

We propose a new method to study the internal memory used by reinforcement learning policies. We estimate the amount of relevant past information by estimating mutual information between behavior histories and the current action of an agent. We perform this estimation in the passive setting, that is, we do not intervene but merely observe the natural behavior of the agent. Moreover, we provide a theoretical justification for our approach by showing that it yields an implementation-independent lower bound on the minimal memory capacity of any agent that implement the observed policy. We demonstrate our approach by estimating the use of memory of DQN policies on concatenated Atari frames, demonstrating sharply different use of memory across 49 games. The study of memory as information that flows from the past to the current action opens avenues to understand and improve successful reinforcement learning algorithms.

Experiments that study neural encoding of stimuli at the level of individual neurons typically choose a small set of features present in the world --- contrast and luminance for vision, pitch and intensity for sound --- and assemble a stimulus set that systematically varies along these dimensions. Subsequent analysis of neural responses to these stimuli typically focuses on regression models, with experimenter-controlled features as predictors and spike counts or firing rates as responses. Unfortunately, this approach requires knowledge in advance about the relevant features coded by a given population of neurons. For domains as complex as social interaction or natural movement, however, the relevant feature space is poorly understood, and an arbitrary \emph{a priori} choice of features may give rise to confirmation bias. Here, we present a Bayesian model for exploratory data analysis that is capable of automatically identifying the features present in unstructured stimuli based solely on neuronal responses. Our approach is unique within the class of latent state space models of neural activity in that it assumes that firing rates of neurons are sensitive to multiple discrete time-varying features tied to the \emph{stimulus}, each of which has Markov (or semi-Markov) dynamics. That is, we are modeling neural activity as driven by multiple simultaneous stimulus features rather than intrinsic neural dynamics. We derive a fast variational Bayesian inference algorithm and show that it correctly recovers hidden features in synthetic data, as well as ground-truth stimulus features in a prototypical neural dataset. To demonstrate the utility of the algorithm, we also apply it to cluster neural responses and demonstrate successful recovery of features corresponding to monkeys and faces in the image set.

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, it is relatively insufficient to empower the discriminative ability of DGMs on making accurate predictions. This paper presents max-margin deep generative models (mmDGMs) and a class-conditional variant (mmDCGMs), which explore the strongly discriminative principle of max-margin learning to improve the predictive performance of DGMs in both supervised and semi-supervised learning, while retaining the generative capability. In semi-supervised learning, we use the predictions of a max-margin classifier as the missing labels instead of performing full posterior inference for efficiency; we also introduce additional max-margin and label-balance regularization terms of unlabeled data for effectiveness. We develop an efficient doubly stochastic subgradient algorithm for the piecewise linear objectives in different settings. Empirical results on various datasets demonstrate that: (1) max-margin learning can significantly improve the prediction performance of DGMs and meanwhile retain the generative ability; (2) in supervised learning, mmDGMs are competitive to the best fully discriminative networks when employing convolutional neural networks as the generative and recognition models; and (3) in semi-supervised learning, mmDCGMs can perform efficient inference and achieve state-of-the-art classification results on several benchmarks.

Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus (LC) approach which allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops. Furthermore, we also design an efficient rejection-free MCMC scheme for approximating the full series. The main novelty underlying our design is in utilizing the concept of cycle basis, which provides an efficient decomposition of the generalized loops. In essence, the proposed MCMC schemes run on transformed GM built upon the non-trivial BP solution, and our experiments show that this synthesis of BP and MCMC outperforms both direct MCMC and bare BP schemes.