All three of us are authors of the PyMC Probabilistic Programming Language, a production grade package used at leading organizations around the world. Ravin learned the power of Bayes Theorem at SpaceX when improving the supply chains of the world's most advanced rockets. He's now an advocate of applied Bayesian methods and has since authored a textbook about Bayes Theorem and writes about appllied data science on his blog. Thomas is enthusiastic about teaching statistics using code and examples, rather than arduous math. Through his many talks and blog posts, he has shown that there is a different way to teach statistics.

The discrete case, generally known as a Markov chain, is discussed on this page. The Markov approach can be applied to the random behaviour of systems that vary discretely or continuously with respect to time and space. This discrete or continuous random variable is known as a stochastic process. Not all stochastic processes can be modelled using the basic Markov approach although there are techniques available for modelling some additional stochastic processes using extensions of this basic method. In order for the basic Markov approach to be applicable, the behaviour of the system must be characterized by a lack of memory, that is, the future states of a system are independent of all past states' except the immediately preceding one.

The rise of the new generation of cyber threats demands more sophisticated and intelligent cyber defense solutions equipped with autonomous agents capable of learning to make decisions without the knowledge of human experts. Several reinforcement learning methods (e.g., Markov) for automated network intrusion tasks have been proposed in recent years. In this paper, we introduce a new generation of network intrusion detection methods that combines a Q-learning-based reinforcement learning with a deep-feed forward neural network method for network intrusion detection. Our proposed Deep Q-Learning (DQL) model provides an ongoing auto-learning capability for a network environment that can detect different types of network intrusions using an automated trial-error approach and continuously enhance its detection capabilities. We provide the details of fine-tuning different hyperparameters involved in the DQL model for more effective self-learning. According to our extensive experimental results based on the NSL-KDD dataset, we confirm that the lower discount factor which is set as 0.001 under 250 episodes of training yields the best performance results. Our experimental results also show that our proposed DQL is highly effective in detecting different intrusion classes and outperforms other similar machine learning approaches.

We review the scholarly contributions that utilise Natural Language Processing (NLP) methods to support the design process. Using a heuristic approach, we collected 223 articles published in 32 journals and within the period 1991-present. We present state-of-the-art NLP in-and-for design research by reviewing these articles according to the type of natural language text sources: internal reports, design concepts, discourse transcripts, technical publications, consumer opinions, and others. Upon summarizing and identifying the gaps in these contributions, we utilise an existing design innovation framework to identify the applications that are currently being supported by NLP. We then propose a few methodological and theoretical directions for future NLP in-and-for design research.

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional probability distributions with score-based diffusion models. In particular, we prove results which provide a theoretical justification for one of the most successful estimators of the conditional score. Moreover, we introduce a multi-speed diffusion framework, which leads to a new estimator for the conditional score, performing on par with previous state-of-the-art approaches. Our theoretical and experimental findings are accompanied by an open source library MSDiff which allows for application and further research of multi-speed diffusion models.

The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may translate to faster, more accurate, and more flexible models, which may directly relate to real-world impact. In this dissertation, we consider two different research areas that concern structuring a learning algorithm's solution: when the structure is known and when it has to be discovered.

Many practical applications of reinforcement learning require agents to learn from sparse and delayed rewards. It challenges the ability of agents to attribute their actions to future outcomes. In this paper, we consider the problem formulation of episodic reinforcement learning with trajectory feedback. It refers to an extreme delay of reward signals, in which the agent can only obtain one reward signal at the end of each trajectory. A popular paradigm for this problem setting is learning with a designed auxiliary dense reward function, namely proxy reward, instead of sparse environmental signals. Based on this framework, this paper proposes a novel reward redistribution algorithm, randomized return decomposition (RRD), to learn a proxy reward function for episodic reinforcement learning. We establish a surrogate problem by Monte-Carlo sampling that scales up least-squares-based reward redistribution to long-horizon problems. We analyze our surrogate loss function by connection with existing methods in the literature, which illustrates the algorithmic properties of our approach. In experiments, we extensively evaluate our proposed method on a variety of benchmark tasks with episodic rewards and demonstrate substantial improvement over baseline algorithms. Scaling reinforcement learning (RL) algorithms to practical applications has become the focus of numerous recent studies, including resource management (Mao et al., 2016), industrial control (Hein et al., 2017), drug discovery (Popova et al., 2018), and recommendation systems (Chen et al., 2018). One of the challenges in these real-world problems is the sparse and delayed environmental rewards. For example, in the molecular structure design problem, the target molecule property can only be evaluated after completing the whole sequence of modification operations (Zhou et al., 2019b). The sparsity of environmental feedback would complicate the attribution of rewards on agent actions and therefore can hinder the efficiency of learning (Rahmandad et al., 2009).

How it works: This algorithm consist of a target / outcome variable (or dependent variable) which is to be predicted from a given set of predictors (independent variables). Using these set of variables, we generate a function that map inputs to desired outputs. The training process continues until the model achieves a desired level of accuracy on the training data. How it works: In this algorithm, we do not have any target or outcome variable to predict / estimate. It is used for clustering population in different groups, which is widely used for segmenting customers in different groups for specific intervention.

In recent years, we've seen a resurgence in AI, or artificial intelligence, and machine learning. Machine learning has led to some amazing results, like being able to analyze medical images and predict diseases on-par with human experts. Google's AlphaGo program was able to beat a world champion in the strategy game go using deep reinforcement learning. Machine learning is even being used to program self driving cars, which is going to change the automotive industry forever. Imagine a world with drastically reduced car accidents, simply by removing the element of human error.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.