相关论文: A Direct Sum Result for the Information Complexity…
Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events,…
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…
We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
We consider the problem of probably approximately correct (PAC) ranking $n$ items by adaptively eliciting subset-wise preference feedback. At each round, the learner chooses a subset of $k$ items and observes stochastic feedback indicating…
Accurate feature detection is fundamental for various computer vision tasks, including autonomous robotics, 3D reconstruction, medical imaging, and remote sensing. Despite advancements in enhancing the robustness of visual features, no…
Probabilistic representation spaces convey information about a dataset and are shaped by factors such as the training data, network architecture, and loss function. Comparing the information content of such spaces is crucial for…
We construct a universally Bayes consistent learning rule that satisfies differential privacy (DP). We first handle the setting of binary classification and then extend our rule to the more general setting of density estimation (with…
Two problems are studied in this paper. (1) How much external or internal information cost is required to compute a Boolean-valued function with an error at most $1/2-\epsilon$ for a small $\epsilon$? It is shown that information cost of…
We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by the joint distribution of an i.i.d. sequence. A random variable $X$ is called informationally infinitely divisible if,…
This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
We dene the distance between two information structures as the largest possible dierence in the value across all zero-sum games. We provide a tractable characterization of the distance, as the minimal distance between 2 polytopes. We use it…
How to measure the complexity of a finite set of vectors embedded in a multidimensional space? This is a non-trivial question which can be approached in many different ways. Here we suggest a set of data complexity measures using universal…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
In communication complexity the input of a function $f:X\times Y\rightarrow Z$ is distributed between two players Alice and Bob. If Alice knows only $x\in X$ and Bob only $y\in Y$, how much information must Alice and Bob share to be able to…
Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity…
Automatic video summarization is still an unsolved problem due to several challenges. We take steps towards making automatic video summarization more realistic by addressing them. Firstly, the currently available datasets either have very…
While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open. The appropriate complexity parameter…