Robots learning from observations in the real world using inverse reinforcement learning (IRL) may encounter objects or agents in the environment, other than the expert, that cause nuisance observations during the demonstration. These confounding elements are typically removed in fully-controlled environments such as virtual simulations or lab settings. When complete removal is impossible the nuisance observations must be filtered out. However, identifying the source of observations when large amounts of observations are made is difficult. To address this, we present a hierarchical Bayesian model that incorporates both the expert's and the confounding elements' observations thereby explicitly modeling the diverse observations a robot may receive. We extend an existing IRL algorithm originally designed to work under partial occlusion of the expert to consider the diverse observations. In a simulated robotic sorting domain containing both occlusion and confounding elements, we demonstrate the model's effectiveness. In particular, our technique outperforms several other comparative methods, second only to having perfect knowledge of the subject's trajectory.

This paper studies the estimation of high-dimensional, discrete, possibly sparse, mixture models in topic models. The data consists of observed multinomial counts of $p$ words across $n$ independent documents. In topic models, the $p\times n$ expected word frequency matrix is assumed to be factorized as a $p\times K$ word-topic matrix $A$ and a $K\times n$ topic-document matrix $T$. Since columns of both matrices represent conditional probabilities belonging to probability simplices, columns of $A$ are viewed as $p$-dimensional mixture components that are common to all documents while columns of $T$ are viewed as the $K$-dimensional mixture weights that are document specific and are allowed to be sparse. The main interest is to provide sharp, finite sample, $\ell_1$-norm convergence rates for estimators of the mixture weights $T$ when $A$ is either known or unknown. For known $A$, we suggest MLE estimation of $T$. Our non-standard analysis of the MLE not only establishes its $\ell_1$ convergence rate, but reveals a remarkable property: the MLE, with no extra regularization, can be exactly sparse and contain the true zero pattern of $T$. We further show that the MLE is both minimax optimal and adaptive to the unknown sparsity in a large class of sparse topic distributions. When $A$ is unknown, we estimate $T$ by optimizing the likelihood function corresponding to a plug in, generic, estimator $\hat{A}$ of $A$. For any estimator $\hat{A}$ that satisfies carefully detailed conditions for proximity to $A$, the resulting estimator of $T$ is shown to retain the properties established for the MLE. The ambient dimensions $K$ and $p$ are allowed to grow with the sample sizes. Our application is to the estimation of 1-Wasserstein distances between document generating distributions. We propose, estimate and analyze new 1-Wasserstein distances between two probabilistic document representations.

Parameter reconstruction is a common problem in optical nano metrology. It generally involves a set of measurements, to which one attempts to fit a numerical model of the measurement process. The model evaluation typically involves to solve Maxwell's equations and is thus time consuming. This makes the reconstruction computationally demanding. Several methods exist for fitting the model to the measurements. On the one hand, Bayesian optimization methods for expensive black-box optimization enable an efficient reconstruction by training a machine learning model of the squared sum of deviations. On the other hand, curve fitting algorithms, such as the Levenberg-Marquardt method, take the deviations between all model outputs and corresponding measurement values into account which enables a fast local convergence. In this paper we present a Bayesian Target Vector Optimization scheme which combines these two approaches. We compare the performance of the presented method against a standard Levenberg-Marquardt-like algorithm, a conventional Bayesian optimization scheme, and the L-BFGS-B and Nelder-Mead simplex algorithms. As a stand-in for problems from nano metrology, we employ a non-linear least-square problem from the NIST Standard Reference Database. We find that the presented method generally uses fewer calls of the model function than any of the competing schemes to achieve similar reconstruction performance.

Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively difficult for such models, given that their flexibility implies that the consequences of prior choices are often relatively opaque. Moreover, these choices can have a substantial effect on posterior inferences. Thus, considerations of robustness need to go hand in hand with nonparametric modeling. In the current paper, we tackle this challenge by exploiting the fact that variational Bayesian methods, in addition to having computational advantages in fitting complex nonparametric models, also yield sensitivities with respect to parametric and nonparametric aspects of Bayesian models. In particular, we demonstrate how to assess the sensitivity of conclusions to the choice of concentration parameter and stick-breaking distribution for inferences under Dirichlet process mixtures and related mixture models. We provide both theoretical and empirical support for our variational approach to Bayesian sensitivity analysis.

State-of-the-art artificial neural networks (ANNs) require labelled data or feedback between layers, are often biologically implausible, and are vulnerable to adversarial attacks that humans are not susceptible to. On the other hand, Hebbian learning in winner-take-all (WTA) networks, is unsupervised, feed-forward, and biologically plausible. However, an objective optimization theory for WTA networks has been missing, except under very limiting assumptions. Here we derive formally such a theory, based on biologically plausible but generic ANN elements. Through Hebbian learning, network parameters maintain a Bayesian generative model of the data. There is no supervisory loss function, but the network does minimize cross-entropy between its activations and the input distribution. The key is a "soft" WTA where there is no absolute "hard" winner neuron, and a specific type of Hebbian-like plasticity of weights and biases. We confirm our theory in practice, where, in handwritten digit (MNIST) recognition, our Hebbian algorithm, SoftHebb, minimizes cross-entropy without having access to it, and outperforms the more frequently used, hard-WTA-based method. Strikingly, it even outperforms supervised end-to-end backpropagation, under certain conditions. Specifically, in a two-layered network, SoftHebb outperforms backpropagation when the training dataset is only presented once, when the testing data is noisy, and under gradient-based adversarial attacks. Adversarial attacks that confuse SoftHebb are also confusing to the human eye. Finally, the model can generate interpolations of objects from its input distribution.

Fully Bayesian approaches to sequential decision-making assume that problem parameters are generated from a known prior, while in practice, such information is often lacking, and needs to be estimated through learning. This problem is exacerbated in decision-making setups with partial information, where using a misspecified prior may lead to poor exploration and inferior performance. In this work we prove, in the context of stochastic linear bandits and Gaussian priors, that as long as the prior estimate is sufficiently close to the true prior, the performance of an algorithm that uses the misspecified prior is close to that of the algorithm that uses the true prior. Next, we address the task of learning the prior through metalearning, where a learner updates its estimate of the prior across multiple task instances in order to improve performance on future tasks. The estimated prior is then updated within each task based on incoming observations, while actions are selected in order to maximize expected reward. In this work we apply this scheme within a linear bandit setting, and provide algorithms and regret bounds, demonstrating its effectiveness, as compared to an algorithm that knows the correct prior. Our results hold for a broad class of algorithms, including, for example, Thompson Sampling and Information Directed Sampling.

Energy-based models (EBMs) are explicit generative models which work by considering Gibbs measures defined through an energy function f, with a probability density proportional to exp( βf(x)), where β is the inverse temperature. Such models originate in statistical physics [Gibbs, 2010, Ruelle, 1969], and have become a fundamental modeling tool in statistics and machine learning [Wainwright and Jordan, 2008, Ranzato et al., 2007, LeCun et al., 2006, Du and Mordatch, 2019, Song and Kingma, 2021]. Given data samples from a target distribution, the learning algorithms for EBMs attempt to estimate an energy function f to model the samples density. The resulting learned model can then be used to obtain new samples, typically through Markov Chain Monte Carlo (MCMC) techniques. The standard method to train EBMs is maximum likelihood estimation, i.e. the learned energy is the one maximizing the likelihood of the target samples, within a certain function class. One generic approach for this is to use gradient descent, where gradients may be approximated using MCMC samples from the trained model. However, this is computationally difficult for highly non-convex trained energies, which in recent years has motivated a myriad of alternative losses to learn EBM energies, such as the popular score matching; see [Song and Kingma, 2021] for a review. EBMs also have structural connections with maximum entropy (maxent) models, which have been studied for decades through Fenchel duality. Dai et al. [2019b] was the first work to leverage similar duality arguments

Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete causal discovery algorithms have been previously introduced, where a directed acyclic graph (DAG), or its equivalence class, representing causal relations is searched. However, in real-world cases, only finite training data is available, which limits the power of statistical tests used by these algorithms, leading to errors in the inferred causal model. This is commonly addressed by devising a strategy for using as few as possible statistical tests. In this paper, we introduce such a strategy in the form of a recursive wrapper for existing constraint-based causal discovery algorithms, which preserves soundness and completeness. It recursively clusters the observed variables using the normalized min-cut criterion from the outset, and uses a baseline causal discovery algorithm during backtracking for learning local sub-graphs. It then combines them and ensures completeness. By an ablation study, using synthetic data, and by common real-world benchmarks, we demonstrate that our approach requires significantly fewer statistical tests, learns more accurate graphs, and requires shorter run-times than the baseline algorithm.

PCA is a dimension reduction method that takes datasets with a large number of features and reduces them to a few underlying features. The sklearn PCA package performs this process for us. In the snippet of code below we are reducing the 75 features that the initial dataset has into 8 features. This snippet serves to show the optimal number of features for the feature reduction algorithm to fit into. The below snippets will show how to use the Gaussian Naive Bayes, Decision Tree, and the K-Nearest Neighbors Classifiers with the reduced features.

'Text Classification' is a Machine Learning technique which is used to analyse text and then organize or categorize them based on patterns or structure. Categorization of text has a lot of applications in the world of artificial intelligence such as news article analysis, hate speech identification, gender classification etc. In this article I use'Text Classification' with Natural Language Processing (NLP) using Python to analyze Hindu religious verses and categorize them. Before we delve deeper into the technical side of Python, let's quickly see what data we will be working with. The'Sahasranama' -- literally 1000 names (where'sahasra' means 1000 and'nama' means names)-- is a hymn of praise offered to God in Hinduism.