Multi Expression Programming (MEP) is a Genetic Programming variant that uses linear chromosomes for solution encoding. A unique feature of MEP is its ability of encoding multiple solutions of a problem in a single chromosome. In this paper we use Multi Expression Programming for evolving digital circuits for a well-known NP-Complete problem: the knapsack (subset sum) problem. Numerical experiments show that Multi Expression Programming performs well on the considered test problems.

One common problem with machine learning algorithms is that we don't know how much training data we need. A common way around this is the often used strategy: keep training until the training error stops decreasing. However, there are still issues with this. How do we know we're not stuck in a local minimum? What if the training error has strange behavior, sometimes staying flat over training iterations but sometimes decreasing sharply?

We study the problem of PAC learning halfspaces on $\mathbb{R}^d$ with Massart noise under Gaussian marginals. In the Massart noise model, an adversary is allowed to flip the label of each point $\mathbf{x}$ with probability $\eta(\mathbf{x}) \leq \eta$, for some parameter $\eta \in [0,1/2]$. The goal of the learner is to output a hypothesis with missclassification error $\mathrm{opt} + \epsilon$, where $\mathrm{opt}$ is the error of the target halfspace. Prior work studied this problem assuming that the target halfspace is homogeneous and that the parameter $\eta$ is strictly smaller than $1/2$. We explore how the complexity of the problem changes when either of these assumptions is removed, establishing the following threshold phenomena: For $\eta = 1/2$, we prove a lower bound of $d^{\Omega (\log(1/\epsilon))}$ on the complexity of any Statistical Query (SQ) algorithm for the problem, which holds even for homogeneous halfspaces. On the positive side, we give a new learning algorithm for arbitrary halfspaces in this regime with sample complexity and running time $O_\epsilon(1) \, d^{O(\log(1/\epsilon))}$. For $\eta <1/2$, we establish a lower bound of $d^{\Omega(\log(1/\gamma))}$ on the SQ complexity of the problem, where $\gamma = \max\{\epsilon, \min\{\mathbf{Pr}[f(\mathbf{x}) = 1], \mathbf{Pr}[f(\mathbf{x}) = -1]\} \}$ and $f$ is the target halfspace. In particular, this implies an SQ lower bound of $d^{\Omega (\log(1/\epsilon) )}$ for learning arbitrary Massart halfspaces (even for small constant $\eta$). We complement this lower bound with a new learning algorithm for this regime with sample complexity and runtime $d^{O_{\eta}(\log(1/\gamma))} \mathrm{poly}(1/\epsilon)$. Taken together, our results qualitatively characterize the complexity of learning halfspaces in the Massart model.

Hypothesis Selection is a fundamental distribution learning problem where given a comparator-class $Q=\{q_1,\ldots, q_n\}$ of distributions, and a sampling access to an unknown target distribution $p$, the goal is to output a distribution $q$ such that $\mathsf{TV}(p,q)$ is close to $opt$, where $opt = \min_i\{\mathsf{TV}(p,q_i)\}$ and $\mathsf{TV}(\cdot, \cdot)$ denotes the total-variation distance. Despite the fact that this problem has been studied since the 19th century, its complexity in terms of basic resources, such as number of samples and approximation guarantees, remains unsettled (this is discussed, e.g., in the charming book by Devroye and Lugosi `00). This is in stark contrast with other (younger) learning settings, such as PAC learning, for which these complexities are well understood. We derive an optimal $2$-approximation learning strategy for the Hypothesis Selection problem, outputting $q$ such that $\mathsf{TV}(p,q) \leq2 \cdot opt + \eps$, with a (nearly) optimal sample complexity of~$\tilde O(\log n/\epsilon^2)$. This is the first algorithm that simultaneously achieves the best approximation factor and sample complexity: previously, Bousquet, Kane, and Moran (COLT `19) gave a learner achieving the optimal $2$-approximation, but with an exponentially worse sample complexity of $\tilde O(\sqrt{n}/\epsilon^{2.5})$, and Yatracos~(Annals of Statistics `85) gave a learner with optimal sample complexity of $O(\log n /\epsilon^2)$ but with a sub-optimal approximation factor of $3$.

AI Researcher, Cognitive Technologist Inventor - AI Thinking, Think Chain Innovator - AIOT, XAI, Autonomous Cars, IIOT Founder Fisheyebox Spatial Computing Savant, Transformative Leader, Industry X.0 Practitioner Understanding neuroscience in terms of #artificialintelligence? It involves affective, behavioral, clinical, cellular, cognitive, computational and systems neuroscience. Computational neuroscience (theoretical neuroscience or mathematical neuroscience) involves machine learning, artificial neural networks, artificial intelligence and computational learning theory. Neuroscientists hope identify correlates of intelligence within the brain and its functioning relying on some brain/head biometrics: brain volume, grey matter volume, white matter volume, white matter integrity, cortical thickness and neural efficiency. They view the understanding of the biological basis of learning, memory, behavior, perception, and consciousness has been described as the "ultimate challenge" of the biological sciences. The substrate of human intelligence has been a topic of considerable interest to philosophers and physicians from the ancient times, and it is known as the mind-body problem, dualism vs monism.

We propose a new approach to SAT solving which solves SAT problems in vector spaces as a cost minimization problem of a non-negative differentiable cost function J^sat. In our approach, a solution, i.e., satisfying assignment, for a SAT problem in n variables is represented by a binary vector u in {0,1}^n that makes J^sat(u) zero. We search for such u in a vector space R^n by cost minimization, i.e., starting from an initial u_0 and minimizing J to zero while iteratively updating u by Newton's method. We implemented our approach as a matrix-based differential SAT solver MatSat. Although existing main-stream SAT solvers decide each bit of a solution assignment one by one, be they of conflict driven clause learning (CDCL) type or of stochastic local search (SLS) type, MatSat fundamentally differs from them in that it continuously approach a solution in a vector space. We conducted an experiment to measure the scalability of MatSat with random 3-SAT problems in which MatSat could find a solution up to n=10^5 variables. We also compared MatSat with four state-of-the-art SAT solvers including winners of SAT competition 2018 and SAT Race 2019 in terms of time for finding a solution, using a random benchmark set from SAT 2018 competition and an artificial random 3-SAT instance set. The result shows that MatSat comes in second in both test sets and outperforms all the CDCL type solvers.

Many scientific conferences employ a two-phase paper review process, where some papers are assigned additional reviewers after the initial reviews are submitted. Many conferences also design and run experiments on their paper review process, where some papers are assigned reviewers who provide reviews under an experimental condition. In this paper, we consider the question: how should reviewers be divided between phases or conditions in order to maximize total assignment similarity? We make several contributions towards answering this question. First, we prove that when the set of papers requiring additional review is unknown, a simplified variant of this problem is NP-hard. Second, we empirically show that across several datasets pertaining to real conference data, dividing reviewers between phases/conditions uniformly at random allows an assignment that is nearly as good as the oracle optimal assignment. This uniformly random choice is practical for both the two-phase and conference experiment design settings. Third, we provide explanations of this phenomenon by providing theoretical bounds on the suboptimality of this random strategy under certain natural conditions. From these easily-interpretable conditions, we provide actionable insights to conference program chairs about whether a random reviewer split is suitable for their conference.

The UW will lead a new artificial intelligence research institute that will focus on fundamental AI and machine learning theory, algorithms and …

Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm. Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm in terms of symmetrized KL information between the input training samples and the output hypothesis. Such a result can be applied to tighten existing expected generalization error bound. Our analysis provides more insight on the fundamental role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.

We extend the theory of PAC learning in a way which allows to model a rich variety of learning tasks where the data satisfy special properties that ease the learning process. For example, tasks where the distance of the data from the decision boundary is bounded away from zero. The basic and simple idea is to consider partial concepts: these are functions that can be undefined on certain parts of the space. When learning a partial concept, we assume that the source distribution is supported only on points where the partial concept is defined. This way, one can naturally express assumptions on the data such as lying on a lower dimensional surface or margin conditions. In contrast, it is not at all clear that such assumptions can be expressed by the traditional PAC theory. In fact we exhibit easy-to-learn partial concept classes which provably cannot be captured by the traditional PAC theory. This also resolves a question posed by Attias, Kontorovich, and Mansour 2019. We characterize PAC learnability of partial concept classes and reveal an algorithmic landscape which is fundamentally different than the classical one. For example, in the classical PAC model, learning boils down to Empirical Risk Minimization (ERM). In stark contrast, we show that the ERM principle fails in explaining learnability of partial concept classes. In fact, we demonstrate classes that are incredibly easy to learn, but such that any algorithm that learns them must use an hypothesis space with unbounded VC dimension. We also find that the sample compression conjecture fails in this setting. Thus, this theory features problems that cannot be represented nor solved in the traditional way. We view this as evidence that it might provide insights on the nature of learnability in realistic scenarios which the classical theory fails to explain.