arXiv research

Two algorithms for interpreting and boosting tree-based models using rule covering.

Invariant Causal Set Covering Machines avoid spurious associations.

We show that hyperelliptic symplectic Lefschetz fibrations are symplectically birational to two-fold covers of rational ruled surfaces, branched in a symplectically embedded surface. This reduces the classification of genus 2 fibrations to the classification of certain symplectic submanifolds in rational ruled surfaces…

We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A r…

The paper proves generalization bounds and stopping rules for self-selected data in reciprocal learning.

ASTRA uses unlabeled data and weak rules to train deep models effectively.

Cannon and Swenson have shown that each hyperbolic 3-manifold group has a natural subdivision rule on the space at infinity, and that this subdivision rule captures the action of the group on the sphere. Explicit subdivision rules have also been found for some closed and finite-volume hyperbolic manifolds, as well as a…

This paper shows that every Gromov hyperbolic group can be described by a finite subdivision rule acting on the 3-sphere. This gives a boundary-like sequence of increasingly refined finite cell complexes which carry all quasi-isometry information about the group. This extends a result from Cannon and Swenson in 1998 th…

This article presents GuideR, a user-guided rule induction algorithm, which overcomes the largest limitation of the existing methods-the lack of the possibility to introduce user's preferences or domain knowledge to the rule learning process. Automatic selection of attributes and attribute ranges often leads to the sit…

This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target …

This paper prices and replicates the financial derivative whose payoff at $T$ is the wealth that would have accrued to a $\$1$ deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the single-stock Black-Scholes market, Ordentlich and Cover (1998) only p…

We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point, the structure of the objective function and the duality gap is used to gather in…

In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the function anywhere in the domain by giving the value of the nearest sample per the …

We consider generalizations of Gale's colored KKM lemma and Shapley's KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions.

CT compares two distributions using Bayes' theorem and chain rule.

Rule-based models are often used for data analysis as they combine interpretability with predictive power. We present RuleKit, a versatile tool for rule learning. Based on a sequential covering induction algorithm, it is suitable for classification, regression, and survival problems. The presence of a user-guided induc…

Designs a Cellular Automata rule for forming touching loop patterns.

We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the `numerator player') picks $b$ so as to maximize $\mathbb{E}[V_t(b)/V_t(c)]$, whil…

Machine learning selects the best prediction rules from noisy data.

Study on 1-Uryson width of polyhedra and their covers.

Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact that this result is model-free, i.e., not dependent on an underlying stochastic …

In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability has been first introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and \cite{KUNIY02} to characterize cla…

We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural nets and by using the technique of chaining mutual information introduced in Asadi…

While the interpretability of machine learning models is often equated with their mere syntactic comprehensibility, we think that interpretability goes beyond that, and that human interpretability should also be investigated from the point of view of cognitive science. The goal of this paper is to discuss to what exten…

We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3-spheres with arbitrarily large injectivity radius. These examples come from a tower of abelian covers of an explicit arithmetic 3-manifold.…

Optimal allocation of human effort to correct AI assessments in decision-making.

This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair randomizations of the initial dollar, by exchanging it for a random wealth whos…

Source code reviews are manual, time-consuming, and expensive. Human involvement should be focused on analyzing the most relevant aspects of the program, such as logic and maintainability, rather than amending style, syntax, or formatting defects. Some tools with linting capabilities can format code automatically and r…

Probabilistic survival predictions from models trained with Maximum Likelihood Estimation (MLE) can have high, and sometimes unacceptably high variance. The field of meteorology, where the paradigm of maximizing sharpness subject to calibration is popular, has addressed this problem by using scoring rules beyond MLE, s…

Let $p\geq 2$ and $q\neq 0$ an integer. A knot $K$ in the three-sphere is said to be a $(p,q)$-lens knot if and only if it covers a link in the lens space $L(p,q)$. In this paper, we use the second coefficient of the HOMFLY polynomial to provide a necessary condition for a knot to be a $(p,q)$-lens knot. As an applicat…

Market maker handles negative prices with unique asset swapping.

This paper proposes an alternative to the classical price-adjustment mechanism (called "tâtonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic equilibration process that depends only on local information. We show how such a proc…

We present sufficient conditions for the cohomology of a closed aspherical manifold to be proper Lipschitz in sense of Connes-Gromov-Moscovici [CGM]. The conditions are stated in terms of the Stone-Čech compactification of the universal cover of a manifold. We show that these conditions are formally weaker than the suf…

Data extracted from software repositories is used intensively in Software Engineering research, for example, to predict defects in source code. In our research in this area, with data from open source projects as well as an industrial partner, we noticed several shortcomings of conventional data mining approaches for c…

Smooth actions on certain 3-spheres can't extend to acyclic 4-manifolds.

Traffic signal control is an important and challenging real-world problem, which aims to minimize the travel time of vehicles by coordinating their movements at the road intersections. Current traffic signal control systems in use still rely heavily on oversimplified information and rule-based methods, although we now …

Machine learning techniques have been used in the past using Monte Carlo samples to construct predictors of the dynamic stability of power systems. In this paper we move beyond the task of prediction and propose a comprehensive approach to use predictors, such as Decision Trees (DT), within a standard optimization fram…

Anchors explain text model decisions by highlighting key words.

In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $θ(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_θ(X)/D(X)$, where $W_θ(X)$ is the…

In recent years, an increasing number of neural network models have included derivatives with respect to inputs in their loss functions, resulting in so-called double backpropagation for first-order optimization. However, so far no general description of the involved derivatives exists. Here, we cover a wide array of s…

New learning rule for quantum measurement classes overcomes uniform convergence issues.

Closed formulas for η-corrections in the once-punctured torus identified.

A spherical topological manifold of dimension n-1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of…

Study presents a method to induce a generalized neural network from joint group invariant functions.

The paper addresses selection bias in conformal prediction for focal units.

We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology…

In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for subagged estimators, both for classification and regressor. General loss functions and class of predictors with both finite and infinite VC-dimension are considered. We slightly generalize the formali…

[Context:] Model-based testing is an instrument for automated generation of test cases. It requires identifying requirements in documents, understanding them syntactically and semantically, and then translating them into a test model. One light-weight language for these test models are Cause-Effect-Graphs (CEG) that ca…