Semantic simultaneous localization and mapping is a subject of increasing interest in robotics and AI that directly influences the autonomous vehicles industry, the army industries, and more. One of the challenges in this field is to obtain object classification jointly with robot trajectory estimation. Considering view-dependent semantic measurements, there is a coupling between different classes, resulting in a combinatorial number of hypotheses. A common solution is to prune hypotheses that have a sufficiently low probability and to retain only a limited number of hypotheses. However, after pruning and renormalization, the updated probability is overconfident with respect to the original probability. This is especially problematic for systems that require high accuracy. If the prior probability of the classes is independent, the original normalization factor can be computed efficiently without pruning hypotheses. To the best of our knowledge, this is the first work to present these results. If the prior probability of the classes is dependent, we propose a lower bound on the normalization factor that ensures cautious results. The bound is calculated incrementally and with similar efficiency as in the independent case. After pruning and updating based on the bound, this belief is shown empirically to be close to the original belief.

This article will explain some of the most well known machine learning algorithms in less than a minute - helping everyone to understand them! One of the simplest Machine learning algorithms out there, Linear Regression is used to make predictions on continuous dependent variables with knowledge from independent variables. A dependent variable is the effect, in which its value depends on changes in the independent variable. You may remember the line of best fit from school - this is what Linear Regression produces. A simple example is predicting one's weight depending on their height.

Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not closed under marginalization, making them poorly equipped to handle systems with latent confounding. Acyclic directed mixed graph (ADMG) models characterize margins of DAG models, making them far better suited to handle such systems. However, ADMG models have not seen wide-spread use due to their complexity and a shortage of statistical tools for their analysis. In this paper, we introduce the m-connecting imset which provides an alternative representation for the independence models induced by ADMGs. Furthermore, we define the m-connecting factorization criterion for ADMG models, characterized by a single equation, and prove its equivalence to the global Markov property. The m-connecting imset and factorization criterion provide two new statistical tools for learning and inference with ADMG models. We demonstrate the usefulness of these tools by formulating and evaluating a consistent scoring criterion with a closed form solution.

We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE) is well-known to be optimal in the limit as $n \to \infty$: it is asymptotically normal with variance matching the Cram\'er-Rao lower bound of $\frac{1}{n\mathcal{I}}$, where $\mathcal{I}$ is the Fisher information of $f$. However, this bound does not hold for finite $n$, or when $f$ varies with $n$. We show for arbitrary $f$ and $n$ that one can recover a similar theory based on the Fisher information of a smoothed version of $f$, where the smoothing radius decays with $n$.

Rule set learning has long been studied and has recently been frequently revisited due to the need for interpretable models. Still, existing methods have several shortcomings: 1) most recent methods require a binary feature matrix as input, while learning rules directly from numeric variables is understudied; 2) existing methods impose orders among rules, either explicitly or implicitly, which harms interpretability; and 3) currently no method exists for learning probabilistic rule sets for multi-class target variables (there is only one for probabilistic rule lists). We propose TURS, for Truly Unordered Rule Sets, which addresses these shortcomings. We first formalize the problem of learning truly unordered rule sets. To resolve conflicts caused by overlapping rules, i.e., instances covered by multiple rules, we propose a novel approach that exploits the probabilistic properties of our rule sets. We next develop a two-phase heuristic algorithm that learns rule sets by carefully growing rules. An important innovation is that we use a surrogate score to take the global potential of the rule set into account when learning a local rule. Finally, we empirically demonstrate that, compared to non-probabilistic and (explicitly or implicitly) ordered state-of-the-art methods, our method learns rule sets that not only have better interpretability but also better predictive performance.

The most difficult task in machine learning is to interpret trained shallow neural networks. Deep neural networks (DNNs) provide impressive results on a larger number of tasks, but it is generally still unclear how decisions are made by such a trained deep neural network. Providing feature importance is the most important and popular interpretation technique used in shallow and deep neural networks. In this paper, we develop an algorithm extending the idea of Garson Algorithm to explain Deep Belief Network based Auto-encoder (DBNA). It is used to determine the contribution of each input feature in the DBN. It can be used for any kind of neural network with many hidden layers. The effectiveness of this method is tested on both classification and regression datasets taken from literature. Important features identified by this method are compared against those obtained by Wald chi square (\c{hi}2). For 2 out of 4 classification datasets and 2 out of 5 regression datasets, our proposed methodology resulted in the identification of better-quality features leading to statistically more significant results vis-\`a-vis Wald \c{hi}2.

Building on the framework introduced by Xu and Raginksy [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define minimum Bayesian regret (MBR) as the difference between the maximum expected cumulative reward obtainable either by learning from the collected data or by knowing the environment and its dynamics. We specialize this definition to reinforcement learning problems modeled as Markov decision processes (MDPs) whose kernel parameters are unknown to the agent and whose uncertainty is expressed by a prior distribution. One method for deriving upper bounds on the MBR is presented and specific bounds based on the relative entropy and the Wasserstein distance are given. We then focus on two particular cases of MDPs, the multi-armed bandit problem (MAB) and the online optimization with partial feedback problem. For the latter problem, we show that our bounds can recover from below the current information-theoretic bounds by Russo and Van Roy [2].

Finding a globally optimal Bayesian Network using exhaustive search is a problem with super-exponential complexity, which severely restricts the number of variables that it can work for. We implement a dynamic programming based algorithm with built-in dimensionality reduction and parent set identification. This reduces the search space drastically and can be applied to large-dimensional data. We use what we call generational orderings based search for optimal networks, which is a novel way to efficiently search the space of possible networks given the possible parent sets. The algorithm supports both continuous and categorical data, and categorical as well as survival outcomes. We demonstrate the efficacy of our algorithm on both synthetic and real data. In simulations, our algorithm performs better than three state-of-art algorithms that are currently used extensively. We then apply it to an Ovarian Cancer gene expression dataset with 513 genes and a survival outcome. Our algorithm is able to find an optimal network describing the disease pathway consisting of 6 genes leading to the outcome node in a few minutes on a basic computer. Our generational orderings based search for optimal networks, is both efficient and highly scalable approach to finding optimal Bayesian Networks, that can be applied to 1000s of variables. Using specifiable parameters - correlation, FDR cutoffs, and in-degree - one can increase or decrease the number of nodes and density of the networks. Availability of two scoring option-BIC and Bge-and implementation of survival outcomes and mixed data types makes our algorithm very suitable for many types of high dimensional biomedical data to find disease pathways.

In the previous post we have learnt about the importance of Latent Variables in Bayesian modelling. Now starting from this post, we will see Bayesian in action. We will walk through different aspects of machine learning and see how Bayesian methods will help us in designing the solutions. And also the additional capabilities and insights we can have by using it. The sections which follows are generally known as Bayesian inference.

The Internet of Things (IoT) has altered living by controlling devices/things over the Internet. IoT has specified many smart solutions for daily problems, transforming cyber-physical systems (CPS) and other classical fields into smart regions. Most of the edge devices that make up the Internet of Things have very minimal processing power. To bring down the IoT network, attackers can utilise these devices to conduct a variety of network attacks. In addition, as more and more IoT devices are added, the potential for new and unknown threats grows exponentially. For this reason, an intelligent security framework for IoT networks must be developed that can identify such threats. In this paper, we have developed an unsupervised ensemble learning model that is able to detect new or unknown attacks in an IoT network from an unlabelled dataset. The system-generated labelled dataset is used to train a deep learning model to detect IoT network attacks. Additionally, the research presents a feature selection mechanism for identifying the most relevant aspects in the dataset for detecting attacks. The study shows that the suggested model is able to identify the unlabelled IoT network datasets and DBN (Deep Belief Network) outperform the other models with a detection accuracy of 97.5% and a false alarm rate of 2.3% when trained using labelled dataset supplied by the proposed approach.