Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We continue a line of research initiated in [10,11]on privacy-preserving statistical databases. Consider a trusted server that holds a database of sensitive information. Given a query function f mapping databases to reals, the so-called true answer is the result of applying f to the database. To protect privacy, the true answer is perturbed by the addition of random noise generated according to a carefully chosen distribution, and this response, the true answer plus noise, is returned to the user.

Previous work focused on the case of noisy sums, in which f = ∑ig(xi), where xi denotes the ith row of the database and g maps database rows to [0,1]. We extend the study to general functions f, proving that privacy can be preserved by calibrating the standard deviation of the noise according to the sensitivity of the function f. Roughly speaking, this is the amount that any single argument to f can change its output. The new analysis shows that for several particular applications substantially less noise is needed than was previously understood to be the case.

The first step is a very clean characterization of privacy in terms of indistinguishability of transcripts. Additionally, we obtain separation results showing the increased value of interactive sanitization mechanisms over non-interactive.

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Calibrating noise to sensitivity in private data analysis

In 1977 Dalenius articulated a desideratum for statistical databases: nothing about an individual should be learnable from the database that cannot be learned without access to the database. We give a general impossibility result showing that a formalization of Dalenius' goal along the lines of semantic security cannot be achieved. Contrary to intuition, a variant of the result threatens the privacy even of someone not in the database. This state of affairs suggests a new measure, differential privacy, which, intuitively, captures the increased risk to one's privacy incurred by participating in a database. The techniques developed in a sequence of papers [8, 13, 3], culminating in those described in [12], can achieve any desired level of privacy under this measure. In many cases, extremely accurate information about the database can be provided while simultaneously ensuring very high levels of privacy

Differential privacy

Publishing data about individuals without revealing sensitive information about them is an important problem. In recent years, a new definition of privacy called k-anonymity has gained popularity. In a k-anonymized dataset, each record is indistinguishable from at least k − 1 other records with respect to certain identifying attributes.In this article, we show using two simple attacks that a k-anonymized dataset has some subtle but severe privacy problems. First, an attacker can discover the values of sensitive attributes when there is little diversity in those sensitive attributes. This is a known problem. Second, attackers often have background knowledge, and we show that k-anonymity does not guarantee privacy against attackers using background knowledge. We give a detailed analysis of these two attacks, and we propose a novel and powerful privacy criterion called e-diversity that can defend against such attacks. In addition to building a formal foundation for e-diversity, we show in an experimental evaluation that e-diversity is practical and can be implemented efficiently.

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L-diversity: Privacy beyond k-anonymity

We continue a line of research initiated in [10, 11] on privacy-preserving statistical databases. Consider a trusted server that holds a database of sensitive information. Given a query function f mapping databases to reals, the so-called true answer is the result of applying f to the database. To protect privacy, the true answer is perturbed by the addition of random noise generated according to a carefully chosen distribution, and this response, the true answer plus noise, is returned to the user. Previous work focused on the case of noisy sums, in which f = Σ i g(x i ), where x i denotes the ith row of the database and g maps database rows to [0,1]. We extend the study to general functions f, proving that privacy can be preserved by calibrating the standard deviation of the noise according to the sensitivity of the function f. Roughly speaking, this is the amount that any single argument to f can change its output. The new analysis shows that for several particular applications substantially less noise is needed than was previously understood to be the case. The first step is a very clean characterization of privacy in terms of indistinguishability of transcripts. Additionally, we obtain separation results showing the increased value of interactive sanitization mechanisms over non-interactive.

There has been increasing interest in the problem of building accurate data mining models over aggregate data, while protecting privacy at the level of individual records. One approach for this problem is to randomize the values in individual records, and only disclose the randomized values. The model is then built over the randomized data, after first compensating for the randomization (at the aggregate level). This approach is potentially vulnerable to privacy breaches: based on the distribution of the data, one may be able to learn with high confidence that some of the randomized records satisfy a specified property, even though privacy is preserved on average.In this paper, we present a new formulation of privacy breaches, together with a methodology, "amplification", for limiting them. Unlike earlier approaches, amplification makes it is possible to guarantee limits on privacy breaches without any knowledge of the distribution of the original data. We instantiate this methodology for the problem of mining association rules, and modify the algorithm from [9] to limit privacy breaches without knowledge of the data distribution. Next, we address the problem that the amount of randomization required to avoid privacy breaches (when mining association rules) results in very long transactions. By using pseudorandom generators and carefully choosing seeds such that the desired items from the original transaction are present in the randomized transaction, we can send just the seed instead of the transaction, resulting in a dramatic drop in communication and storage cost. Finally, we define new information measures that take privacy breaches into account when quantifying the amount of privacy preserved by randomization.

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Limiting privacy breaches in privacy preserving data mining

We present a framework for mining association rules from transactions consisting of categorical items where the data has been randomized to preserve privacy of individual transactions. While it is feasible to recover association rules and preserve privacy using a straightforward "uniform" randomization, the discovered rules can unfortunately be exploited to find privacy breaches. We analyze the nature of privacy breaches and propose a class of randomization operators that are much more effective than uniform randomization in limiting the breaches. We derive formulae for an unbiased support estimator and its variance, which allow us to recover itemset supports from randomized datasets, and show how to incorporate these formulae into mining algorithms. Finally, we present experimental results that validate the algorithm by applying it on real datasets.

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Privacy preserving mining of association rules

Literature on information integration across databases tacitly assumes that the data in each database can be revealed to the other databases. However, there is an increasing need for sharing information across autonomous entities in such a way that no information apart from the answer to the query is revealed. We formalize the notion of minimal information sharing across private databases, and develop protocols for intersection, equijoin, intersection size, and equijoin size. We also show how new applications can be built using the proposed protocols.

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Information sharing across private databases

The rising need for custom machine learning (ML) algorithms and the growing data sizes that require the exploitation of distributed, data-parallel frameworks such as MapReduce or Spark, pose significant productivity challenges to data scientists. Apache SystemML addresses these challenges through declarative ML by (1) increasing the productivity of data scientists as they are able to express custom algorithms in a familiar domain-specific language covering linear algebra primitives and statistical functions, and (2) transparently running these ML algorithms on distributed, data-parallel frameworks by applying cost-based compilation techniques to generate efficient, low-level execution plans with in-memory single-node and large-scale distributed operations. This paper describes SystemML on Apache Spark, end to end, including insights into various optimizer and runtime techniques as well as performance characteristics. We also share lessons learned from porting SystemML to Spark and declarative ML in general. Finally, SystemML is open-source, which allows the database community to leverage it as a testbed for further research.

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SystemML: declarative machine learning on spark

Suppose there are many clients, each having some personal information, and one server, which is interested only in aggregate, statistically significant, properties of this information. The clients can protect privacy of their data by perturbing it with a randomization algorithm and then submitting the randomized version. The randomization algorithm is chosen so that aggregate properties of the data can be recovered with sufficient precision, while individual entries are significantly distorted. How much distortion is needed to protect privacy can be determined using a privacy measure. Several possible privacy measures are known; finding the best measure is an open question. This paper presents some methods and results in randomization for numerical and categorical data, and discusses the issue of measuring privacy.

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Alexandre V. Evfimievski

Papers

Limiting privacy breaches in privacy preserving data mining

Privacy preserving mining of association rules

Information sharing across private databases

SystemML: declarative machine learning on spark

Randomization in privacy preserving data mining