One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find \textit{invariant representations} of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of $\epsilon$-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds \textit{probabilistically} over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Computational Learning Theory: 15th Annual Conference on Computational Learning Theory, COLT 2002, Sydney, Australia, July 8-10, 2002. Proceedings (Lecture Notes in Computer Science, 2375) [Kivinen, Jyrki, Sloan, Robert H.] on Amazon.com. *FREE* shipping on qualifying offers. Computational Learning Theory: 15th Annual Conference on Computational Learning Theory, COLT 2002, Sydney, Australia, July 8-10, 2002. Proceedings (Lecture Notes in Computer Science, 2375)

Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning. Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs.

Computational Learning Theory: Third European Conference, EuroCOLT '97, Jerusalem, Israel, March 17 - 19, 1997, Proceedings (Lecture Notes in Computer Science, 1208) [Ben-David, Shai] on Amazon.com. *FREE* shipping on qualifying offers. Computational Learning Theory: Third European Conference, EuroCOLT '97, Jerusalem, Israel, March 17 - 19, 1997, Proceedings (Lecture Notes in Computer Science, 1208)

We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(\mathbf{x}, y) \in \mathbb{R}^N \times \{ \pm 1\}$, where the distribution of $\mathbf{x}$ is arbitrary and the label $y$ is a Massart corruption of $f(\mathbf{x})$, for an unknown halfspace $f: \mathbb{R}^N \to \{ \pm 1\}$, with flipping probability $\eta(\mathbf{x}) \leq \eta < 1/2$. The goal of the learner is to compute a hypothesis with small 0-1 error. Our main result is the first computational hardness result for this learning problem. Specifically, assuming the (widely believed) subexponential-time hardness of the Learning with Errors (LWE) problem, we show that no polynomial-time Massart halfspace learner can achieve error better than $\Omega(\eta)$, even if the optimal 0-1 error is small, namely $\mathrm{OPT} = 2^{-\log^{c} (N)}$ for any universal constant $c \in (0, 1)$. Prior work had provided qualitatively similar evidence of hardness in the Statistical Query model. Our computational hardness result essentially resolves the polynomial PAC learnability of Massart halfspaces, by showing that known efficient learning algorithms for the problem are nearly best possible.

In order to learn efficiently in a complex world with multiple, sometimes rapidly changing objectives, both animals and machines must leverage information obtained from past experience. This is a challenging task, as processing and storing all relevant information is computationally infeasible. How can an intelligent agent address this problem? We hypothesize that one route may lie in the dual process theory of cognition, a longstanding framework in cognitive psychology first introduced by William James (James, 1890) which lies at the heart of many dichotomies in both cognitive science and machine learning. Examples include goal-directed versus habitual behavior (Graybiel, 2008), model-based versus model-free reinforcement learning (Daw et al., 2011; Sutton and Barto, 2018), and "System 1" versus "System 2" thinking (Kahneman, 2011).

We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related notion of strong CPAC learning, and provide a negative answer to the COLT open problem posed by Agarwal et al. (2021) whether all decidably representable VC classes are improperly CPAC learnable. Second, we consider undecidability of (computable) PAC learnability. We give a simple general argument to exhibit such undecidability, and initiate a study of the arithmetical complexity of learnability. We briefly discuss the relation to the undecidability result of Ben-David et al. (2019), that motivated the work of Agarwal et al.

Symbolic regression (SR) is the task of learning a model of data in the form of a mathematical expression. By their nature, SR models have the potential to be accurate and human-interpretable at the same time. Unfortunately, finding such models, i.e., performing SR, appears to be a computationally intensive task. Historically, SR has been tackled with heuristics such as greedy or genetic algorithms and, while some works have hinted at the possible hardness of SR, no proof has yet been given that SR is, in fact, NP-hard. This begs the question: Is there an exact polynomial-time algorithm to compute SR models? We provide evidence suggesting that the answer is probably negative by showing that SR is NP-hard.

Soft skills: Amazon interview preparation guide, principles Amazon expects in their employees, Amazon principles explained, Situation Task Action Result technique, soft skills from a machine learning PhD; Coding: coding interview preparation leetcode, Cracking the Coding interview book, practicing machine learning problems; Machine learning theory: Machine Learning QA book 1, Machine Learning QA book 2, summary from glassdoor, when not to use machine learning, methods section of paperswithcode. If you liked this article share it with a friend! To read more on machine learning and image processing topics press subscribe!

For an algorithm to be termed "efficient", its execution time must be constrained by a polynomial function of the input size. It was realised early on that not all issues could be handled thus rapidly, but it was difficult to determine which ones could and which couldn't. Some so-called NP-hard issues are thought to be impossible to answer in polynomial time. NP-hard stands for non-deterministic polynomial-time hardness. This article will be focused on understanding some NP-hard problems and trying to solve them with Reinforcement Learning. Following are the topics to be covered.