The satisfiability problem is one of the most famous problems in computer science. Its NP-completeness has been used to argue that SAT is intractable. However, there have been tremendous advances that allow SAT solvers to solve instances with millions of variables. A particularly successful paradigm is stochastic local search. In most cases, there are different ways of formulating the underlying problem. While it is known that this has an impact on the runtime of solvers, finding a helpful formulation is generally non-trivial. The recently introduced GapSAT solver [Lorenz and W\"orz 2020] demonstrated a successful way to improve the performance of an SLS solver on average by learning additional information which logically entails from the original problem. Still, there were cases in which the performance slightly deteriorated. This justifies in-depth investigations into how learning logical implications affects runtimes for SLS. In this work, we propose a method for generating logically equivalent problem formulations, generalizing the ideas of GapSAT. This allows a rigorous mathematical study of the effect on the runtime of SLS solvers. If the modification process is treated as random, Johnson SB distributions provide a perfect characterization of the hardness. Since the observed Johnson SB distributions approach lognormal distributions, our analysis also suggests that the hardness is long-tailed. As a second contribution, we theoretically prove that restarts are useful for long-tailed distributions. This implies that additional restarts can further refine all algorithms employing above mentioned modification technique. Since the empirical studies compellingly suggest that the runtime distributions follow Johnson SB distributions, we investigate this property theoretically. We succeed in proving that the runtimes for Sch\"oning's random walk algorithm are approximately Johnson SB.

A critical element in the development and deployment of AVs is the design of car-following (CF) controllers capable of producing desirable performance in real-world settings. Ideally, a CF control system would effectively and safely handle the longitudinal maneuvers of the vehicle at every encounter it faces. However, designing and training such a controller requires enormous data, testing, and experimentation that covers all possible driving scenarios/encounters. In other words, it requires us to have a perfect understanding of the environment these AVs would be operating under. Clearly, this is very challenging and, possibly, unattainable. AVs are likely to encounter unseen scenarios and be exposed to exogenous and endogenous uncertainties in the physical world. The sources of exogenous and endogenous uncertainties are vast and roughly classified into (Macfarlane and Stroila, 2016; Yao et al., 2020; Katrakazas et al., 2015): (i) vehicular and system dynamics (e.g., vehicle condition, road gradient, aerodynamic drag force, external loads, transmission, brake, the performance of the engine, etc.), (ii) environmental conditions (snow, dust, wind, wet conditions, etc.), and (iii) situational detection (e.g., sensor/measurement errors, radar errors, vehicle speed fluctuations, vehicle localization, communication latency, etc.). All these types of uncertainties can hinder desirable performance (e.g., stability). Yet, a major challenge lies in the complexity of integrating these uncertainties into the control system and the design of the AV.

The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given context and an action taken by an agent. In contrast to Bayesian optimization, the arguments of the function are not under agent's control, but are indirectly determined by the agent's action based on a given context. If the information of the features is to be included in the maximization problem, the full conditional distribution of such features, rather than its expectation only, needs to be accounted for. Furthermore, the function is itself unknown, only counting with noisy observations of such function, and potentially requiring the use of unmatched data sets. We propose a novel algorithm for the aforementioned problem which takes into consideration the uncertainty derived from the estimation of both the conditional distribution of the features and the unknown function, by modeling the former as a Bayesian conditional mean embedding and the latter as a Gaussian process. Our algorithm empirically outperforms the current state-of-the-art algorithm in the experiments conducted.

Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. In this manuscript, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl's do-calculus, and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. The code and the data documenting all the case studies are available at \url{https://github.com/srtaheri/LVMwithDoCalculus}

When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and specifically the No-U-Turn Sampler (NUTS) which automatically decides the end time of the Hamiltonian trajectory. However, HMC and NUTS can require numerous numerical gradients of the target density, and can prove slow in practice. We propose Hamiltonian neural networks (HNNs) with HMC and NUTS for solving Bayesian inference problems. Once trained, HNNs do not require numerical gradients of the target density during sampling. Moreover, they satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well-suited for use within HMC and NUTS because stationarity can be shown. We also propose an HNN extension called latent HNNs (L-HNNs), which are capable of predicting latent variable outputs. Compared to HNNs, L-HNNs offer improved expressivity and reduced integration errors. Finally, we employ L-HNNs in NUTS with an online error monitoring scheme to prevent sample degeneracy in regions of low probability density. We demonstrate L-HNNs in NUTS with online error monitoring on several examples involving complex, heavy-tailed, and high-local-curvature probability densities. Overall, L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring required 1--2 orders of magnitude fewer numerical gradients of the target density and improved the effective sample size (ESS) per gradient by an order of magnitude.

Abstract-- Robotic manipulation stands as a largely unsolved problem despite significant advances in robotics and machine learning in recent years. One of the key challenges in manipulation is the exploration of the dynamics of the environment when there is continuous contact between the objects being manipulated. This paper proposes a model-based active exploration approach that enables efficient learning in sparse-reward robotic manipulation tasks. The proposed method estimates an information gain objective using an ensemble of probabilistic models and deploys model predictive control (MPC) to plan actions online that maximize the expected reward while also performing directed exploration. We evaluate our proposed algorithm in simulation and on a real robot, trained from Figure 1: Our active exploration strategy evaluated on a challenging scratch with our method, on a challenging ball pushing task Tilted Pushing task in simulation (left) and on the real robot (right). Our real-world robot experiment serves as sparse reward model in order to bring the ball to a target location. We believe that for of dexterous manipulation capabilities was one of the major robots to reach human-level manipulation skills, they must driving factors in the development of the human mind [1] actively explore and adapt to new instances of a task. Performing manipulation is cognitively highly demanding, forcing the We define active exploration as the directed search of the agent to reason not only about the impact of its actions on agent, during the learning process, for unvisited state-action itself, but also on the environment. This inherent complexity pairs that would maximize the agent's performance.

Mobile robots have been widely used in various aspects of human life. When a robot moves between different positions in the working area to perform the task, controlling motion to follow a pre-defined path is the primary task of a mobile robot. Furthermore, the robot must remain at its desired speed to cooperate with other agents. This paper presents a development of a motion controller, in which the fuzzy logic method is combined with a kinematic model of a differential drive robot. The simulation results are compared well with experimental results indicate that the method is effective and applicable for actual mobile robots.

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in practice. Under label corruptions, we prove that this simple estimator achieves minimax near-optimal risk on a wide range of generalized linear models, including Gaussian regression, Poisson regression and Binomial regression. Finally, we extend the estimator to the more challenging setting of label and covariate corruptions and demonstrate its robustness and optimality in that setting as well.

Each machine learning algorithm handles one specific problem, and this way beginners can dive into one of these to figure out solutions, one at a time. Here is a compilation of the top machine learning algorithms that are frequently used in all machine learning fields. Now, you can practice ML algorithms here. Forming relationships between two variables is almost the starting point of a model, and linear regression in machine learning achieves that. The relationship between the dependent and independent variables is established by aligning them on a regression line.

Explainable Artificial Intelligence (XAI) is a paradigm that delivers transparent models and decisions, which are easy to understand, analyze, and augment by a non-technical audience. Fuzzy Logic Systems (FLS) based XAI can provide an explainable framework, while also modeling uncertainties present in real-world environments, which renders it suitable for applications where explainability is a requirement. However, most real-life processes are not characterized by high levels of uncertainties alone; they are inherently time-dependent as well, i.e., the processes change with time. In this work, we present novel Temporal Type-2 FLS Based Approach for time-dependent XAI (TXAI) systems, which can account for the likelihood of a measurement's occurrence in the time domain using (the measurement's) frequency of occurrence. In Temporal Type-2 Fuzzy Sets (TT2FSs), a four-dimensional (4D) time-dependent membership function is developed where relations are used to construct the inter-relations between the elements of the universe of discourse and its frequency of occurrence. The TXAI system manifested better classification prowess, with 10-fold test datasets, with a mean recall of 95.40\% than a standard XAI system (based on non-temporal general type-2 (GT2) fuzzy sets) that had a mean recall of 87.04\%. TXAI also performed significantly better than most non-explainable AI systems between 3.95\%, to 19.04\% improvement gain in mean recall. In addition, TXAI can also outline the most likely time-dependent trajectories using the frequency of occurrence values embedded in the TXAI model; viz. given a rule at a determined time interval, what will be the next most likely rule at a subsequent time interval. In this regard, the proposed TXAI system can have profound implications for delineating the evolution of real-life time-dependent processes, such as behavioural or biological processes.