Model interpretability is an increasingly important component of practical machine learning. Some of the most common forms of interpretability systems are example-based, local, and global explanations. One of the main challenges in interpretability is designing explanation systems that can capture aspects of each of these explanation types, in order to develop a more thorough understanding of the model. We address this challenge in a novel model called SLIM that uses local linear modeling techniques along with a dual interpretation of random forests (both as a supervised neighborhood approach and as a feature selection method). SLIM has two fundamental advantages over existing interpretability systems. First, while it is effective as a black-box explanation system, SLIM itself is a highly accurate predictive model that provides faithful self explanations, and thus sidesteps the typical accuracy-interpretability trade-off. Second, SLIM provides both example- based and local explanations and can detect global patterns, which allows it to diagnose limitations in its local explanations.
We say that a function is if it is human simulatable @cite_5 . This definition requires that a person can 1) carry out all of the model calculations in reasonable time, which rules out functions that are too complicated, and 2) provide a semantic description of each calculation, which rules out using features that do not have well understood meanings. Generally, sparse-linear models, small decision trees, nearest neighbors, and short rule lists are all considered to be human simulatable.
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2952554977 2059100041 1991143958 49730540
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to compute arbitrarily close piece-wise interval approximations. Even though this fragment is undecidable, we prove that there is a (possibly non-terminating) algorithm for checking satisfiability such that (1) whenever it terminates, it computes a correct answer, and (2) it always terminates when the input is robust. A formula is robust, if its satisfiability does not change under small perturbations. As a basic tool for our algorithm we use the notion of degree from the field of (differential) topology. In a glance, we can perceive whether a stack of dishes will topple, a branch will support a child’s weight, a grocery bag is poorly packed and liable to tear or crush its contents, or a tool is firmly attached to a table or free to be lifted. Such rapid physical inferences are central to how people interact with the world and with each other, yet their computational underpinnings are poorly understood. We propose a model based on an “intuitive physics engine,” a cognitive mechanism similar to computer engines that simulate rich physics in video games and graphics, but that uses approximate, probabilistic simulations to make robust and fast inferences in complex natural scenes where crucial information is unobserved. This single model fits data from five distinct psychophysical tasks, captures several illusions and biases, and explains core aspects of human mental models and common-sense reasoning that are instrumental to how humans understand their everyday world. Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on ℝN with smoothness of order s can in general be captured with accuracy at most O(n−s N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s is not, then n has to be chosen inordinately large for good accuracy. The large value of N often precludes reasonable numerical procedures. On the other hand, there is the common belief that real world problems in high dimensions have as their solution, functions which are more amenable to numerical recovery. This has led to the introduction of models for these functions that do not depend on smoothness alone but also involve some form of variable reduction. In these models it is assumed that, although the function depends on N variables, only a small number of them are significant. Another variant of this principle is that the function lives on a low dimensional manifold. Since the dominant variables (respectively the manifold) are unknown, this leads to new problems of how to organize point queries to capture such functions. The present paper studies where to query the values of a ridge function f(x)=g(a⋅x) when both a∈ℝN and g∈C[0,1] are unknown. We establish estimates on how well f can be approximated using these point queries under the assumptions that g∈Cs[0,1]. We also study the role of sparsity or compressibility of a in such query problems. Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary first-order sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in first-order logic, providing a way to apply first-order theorem provers to reasoning about non-Herbrand stable models.