Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

Feature matching is at the base of many computer vision problems, such as object recognition or structure from motion. Current methods rely on costly descriptors for detection and matching. In this paper, we propose a very fast binary descriptor based on BRIEF, called ORB, which is rotation invariant and resistant to noise. We demonstrate through experiments how ORB is at two orders of magnitude faster than SIFT, while performing as well in many situations. The efficiency is tested on several real-world applications, including object detection and patch-tracking on a smart phone.

ORB: An efficient alternative to SIFT or SURF

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

/pdf/approximate-nearest-neighbors-towards-removing-the-curse-of-27lmlz5prr.pdf

Approximate nearest neighbors: towards removing the curse of dimensionality

While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced Thus, interpretability of models has been recognized as an equally important quality as their predictive power In particular, rule-based systems are experiencing a renaissance owing to their intuitive if-then representation 
However, simply being rule-based does not ensure interpretability For example, overlapped rules spawn ambiguity and hinder interpretation Here we propose a novel approach of inferring diverse rule sets, by optimizing small overlap among decision rules with a 2-approximation guarantee under the framework of Max-Sum diversification We formulate the problem as maximizing a weighted sum of discriminative quality and diversity of a rule set 
In order to overcome an exponential-size search space of association rules, we investigate several natural options for a small candidate set of high-quality rules, including frequent and accurate rules, and examine their hardness Leveraging the special structure in our formulation, we then devise an efficient randomized algorithm, which samples rules that are highly discriminative and have small overlap The proposed sampling algorithm analytically targets a distribution of rules that is tailored to our objective 
We demonstrate the superior predictive power and interpretability of our model with a comprehensive empirical study against strong baselines

Diverse Rule Sets

Defining appropriate distance measures among rankings is a classic area of study which has led to many useful applications. In this paper, we propose a more general abstraction of preference data, namely directed acyclic graphs (DAGs), and introduce a measure for comparing DAGs, given that a vertex correspondence between the DAGs is known. We study the properties of this measure and use it to aggregate and cluster a set of DAGs. We show that these problems are $$\mathbf {NP}$$NP-hard and present efficient methods to obtain solutions with approximation guarantees. In addition to preference data, these methods turn out to have other interesting applications, such as the analysis of a collection of information cascades in a network. We test the methods on synthetic and real-world datasets, showing that the methods can be used to, e.g., find a set of influential individuals related to a set of topics in a network or to discover meaningful and occasionally surprising clustering structure.

/pdf/beyond-rankings-comparing-directed-acyclic-graphs-2o90rp6f2x.pdf

Beyond rankings: comparing directed acyclic graphs

A matching between content items and consumers is discloses. More particularly, items and consumers are matched using a matching approach that uses capacity constraints associated with each consumer, capacity constraints associated with each item, and relationship weights, each relationship weight representing a similarity between a consumer and an item. Edges representing the relationships between consumers and items can be selected using an iterative selection that includes a matching approach that permits capacity constraints. Alternatively, edges can be selected using an iterative approach that allows a solution to be identified prior to completion of the selection processing.

System and method of matching content items and consumers

In this paper we advocate that market mechanisms inspired by economics in conjunction with intelligent data selection is the key to fulfilling learning tasks in the presence of big data subject to privacy concerns of users. We design a market of private data that are gathered towards building a classifier. Each data owner has a private cost that quantifies his discomfort for providing data to the learner. Also, at each stage of the learning process, each data owner is characterized by a utility score, which expresses the utility of his data for the learner. The learner initiates a call for buying data, and interested owners respond by declaring their costs. The learner computes the utility score of each data owner. It then selects one owner to buy data from and associated payment. For the goals of minimizing the expected privacy cost of users and of minimizing the expected payment by the learner, we propose a variation of a Vickrey-Clarke-Groves (VCG) auction and an optimal auction respectively. For the case where the data arrive in a streaming fashion, we formulate the multi-round sequential decision version of the problem of learning the classifier. At each round the learner decides whether it will stop the learning process given the current classifier accuracy or perform one more auction. The problem amounts to weighing the current cost of classifier inaccuracy against the expected (privacy or reimbursement) costs incurred through the auction, plus the expected cost of the new classifier accuracy, we cast this problem as an optimal stopping one. The complexity of our framework scales only linearly with the size of the data set and fits in a broad range of private-data scenarios and data attributes.

Auctioning Data for Learning

We study a new notion of graph centrality based on absorbing random walks. Given a graph $G=(V,E)$ and a set of query nodes $Q\subseteq V$, we aim to identify the $k$ most central nodes in $G$ with respect to $Q$. Specifically, we consider central nodes to be absorbing for random walks that start at the query nodes $Q$. The goal is to find the set of $k$ central nodes that minimizes the expected length of a random walk until absorption. The proposed measure, which we call $k$ absorbing random-walk centrality, favors diverse sets, as it is beneficial to place the $k$ absorbing nodes in different parts of the graph so as to "intercept" random walks that start from different query nodes. 
Although similar problem definitions have been considered in the literature, e.g., in information-retrieval settings where the goal is to diversify web-search results, in this paper we study the problem formally and prove some of its properties. We show that the problem is NP-hard, while the objective function is monotone and supermodular, implying that a greedy algorithm provides solutions with an approximation guarantee. On the other hand, the greedy algorithm involves expensive matrix operations that make it prohibitive to employ on large datasets. To confront this challenge, we develop more efficient algorithms based on spectral clustering and on personalized PageRank.

Aristides Gionis

Papers

Diverse Rule Sets

Beyond rankings: comparing directed acyclic graphs

System and method of matching content items and consumers

Auctioning Data for Learning

Absorbing random-walk centrality: Theory and algorithms