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Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a…
Generalization remains a central yet unresolved challenge in deep learning, particularly the ability to predict a model's performance beyond its training distribution using quantities available prior to test-time evaluation. Building on the…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
A fundamental problem faced by object recognition systems is that objects and their features can appear in different locations, scales and orientations. Current deep learning methods attempt to achieve invariance to local translations via…
This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…
Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit…
The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID)…
Let F = F_p for any fixed prime p >= 2. An affine-invariant property is a property of functions on F^n that is closed under taking affine transformations of the domain. We prove that all affine-invariant property having local…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…
Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
Property testers are fast randomized algorithms whose task is to distinguish between inputs satisfying some predetermined property ${\cal P}$ and those that are far from satisfying it. Since these algorithms operate by inspecting a small…
Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat…
We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
This work studies the problem of few-shot object counting, which counts the number of exemplar objects (i.e., described by one or several support images) occurring in the query image. The major challenge lies in that the target objects can…
Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…