About me

I am a new member of Microsoft Research New England, a new lab in Cambridge, MA. I have previously been an assistant professor of computer science at Georgia Tech and TTI-Chicago. I was extremely fortunate to receive a PhD at CMU from the ingenious Avrim Blum, followed by an NSF postdoc at MIT under the wise guidance of Santosh Vempala.

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short biography    contact details

My main research interests are machine learning, human computation, and algorithms.

Teaching and Students

Spring 2008: Game Theory and Computer Science, (Georgia Tech)

Fall 2006: Machine Learning Theory (Weizmann Institute)

Autumn 2004: Online Algorithms (University of Chicago)

• Adam Tauman Kalai and Ehud Kalai
  Cooperation in strategic games revisited
  Northwestern University, Center for Mathematical Studies in Economics and Management Science: Discussion Paper #1512
  
abstract   pdf

For two-person strategic games with transferable utility, all major variable-threat bargaining and arbitration solutions coincide. This confluence of solutions by luminaries such as Nash, Raiffa, and Selten, is more than mere coincidence.
The present paper unifies and extends these solution into a complete theory. For two- person strategic games with transferable utility, it presents: (1) a decomposition of a game into cooperative and competitive components, (2) an intuitive and computable closed-form formula for the solution, (3) an axiomatic justification of the solution, and (4) a generalization of the above to games with private signals, along with an arbitration scheme that noncooperatively implements the solution with this type of incomplete information. The objective is to restart research on cooperative solutions to strategic games and their applications.
• Agnostic Learning: Theory and Algorithms. NIPS 2008 Tutorial.
  NIPS conference, with movie
  
abstract   movies

Agnostic Learning (Kearns, Schapire and Sellie '92; Haussler '90) is a branch of Computational Learning Theory in which little or no assumptions are made about the true function being learned. The results are powerful, noise-tolerant binary-classification algorithms. Like Valiant's seminal PAC model, the algorithms are required to be computationally efficient. Unlike the PAC model, it does not assume anything about the "true" labeling function, and hence Agnostic Learning can also be viewed as learning with arbitrary or even adversarial noise. Recent progress has shown that several classical algorithms can be improved and made agnostic. Moreover, the agnostic perspective sheds light on several key Machine Learning notions, such as Fourier learning, SVMs, Active Learning, Decision Tree Learning, and Boosting. Hence, this tutorial on Agnostic Learning also presents an opportunity to overview and reconsider many beautiful notions from Computational Learning Theory.

2011

• Omer Tamuz, Ce Liu, Serge Belongie, Ohad Shamir, and Adam Kalai
  Adaptively Learning the Crowd Kernel
  In Proceedings of the 28th International Conference on Machine Learning (ICML), 2011.
  
abstract   pdf   powerpoint
We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form "is object a more similar to b or to c?" and is chosen to be maximally informative given the preceding responses. The output is an embedding of the objects into Euclidean space (like MDS); we refer to this as the "crowd kernel." SVMs reveal that the crowd kernel captures prominent and subtle features across a number of domains, such as " is striped" among neckties and "vowel vs. consonant" among letters.
• Adam Kalai and Ehud Kalai
  Cooperation in Two Person Games, Revisited
  ACM SIGEcom Exchanges, 10(1):13-16.
  
abstract   pdf
Luminaries such as Nash (1953), Rai a (1953), and Selten (1960), studied cooperation in two-person strategic games. We point out that when players may make monetary side payments, i.e., bimatrix games with transferable utility (TU), all previous solutions coincide. This solution is justified by simple axioms and an elementary decomposition of every such game into a (competitive) zero-sum game and a (cooperative) team game.
• Brendan Juba, Adam Tauman Kalai, Sanjeev Khanna, and Madhu Sudan
  Compression without a Common Prior: an Information-Theoretic Justification for Ambiguity in Natural Language
  In Innovations in Computer Science (ICS), 2011.
  
abstract   pdf
Compression is a fundamental goal of both human language and digital communication, yet natural language is very different from compression schemes employed by modern computers. We partly explain this difference using the fact that information theory generally assumes a common prior probability distribution shared by the encoder and decoder, whereas human communication has to be robust to the fact that a speaker and listener may have different prior beliefs about what a speaker may say. We model this information-theoretically using the following question: what type of compression scheme would be effective when the encoder and decoder have (boundedly) different prior probability distributions. The resulting compression scheme resembles natural language to a far greater extent than existing digital communication protocols. We also use information theory to justify why ambiguity is necessary for the purpose of compression.
• Nicole Immorlica, Adam Tauman Kalai, Brendan Lucier, Ankur Moitra, Andrew Postlewaite, and Moshe Tennenholtz
  Dueling Algorithms
  In Proceedings of the forty-second annual ACM symposium on the Theory of Computing (STOC), 2011.
  
abstract   pdf   press
We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two players, whose only goal is to outperform the opponent. Such games are typically exponentially large zero-sum games, but they often have a rich combinatorial structure. We provide general techniques by which such structure can be leveraged to find minmax-optimal and approximate minmax-optimal strategies. We give examples of ranking, hiring, compression, and binary search duels, among others. We give bounds on how often one can beat the classic optimization algorithms in such duels.

2010

• Adam Tauman Kalai, Ehud Kalai
  Cooperation and competition in strategic games with private information
  June 2010; EC '10: Proceedings of the 11th ACM conference on Electronic commerce.
  abstract   pdf (purchase)
  
We study strategic games in the tradition of cooperative game theory, where players may make binding agreements that involve side payments. We use a decomposition of strategic games into competitive and cooperative components to define and axiomatize a solution that unifies earlier solutions and generalizes to the case of incomplete information. In the latter case, we give incentive compatible mechanisms that achieve first-best efficiency.
• Adam Tauman Kalai, Ankur Moitra and Gregory Valiant
  Efficiently Learning Mixtures of Two Gaussians
  In Proceedings of the forty-first annual ACM symposium on the Theory of Computing (STOC), 2010.
  
abstract   pdf
We consider the basic problem of learning the parameters of a mixture of two arbitrary mutlivariate Gaussians. Under provably minimal assumptions (namely that the mixing weights are bounded from 0 and the statistical distance between the two Gaussians is bounded from 0), we give a polynomial-time algorithm for extimating the mixture parameters that converges at an inverse polynomial rate. Previously, efficient algorithms were known for the special case where the Gaussians had little overlap, namely there statistical distance was close to 1.
• Adam Tauman Kalai, Ehud Kalai, Ehud Lehrer, and Dov Samet
  A Commitment Folk Theorem
  Games and Economic Behavior, 69(1): 127-137, 2010.
  
abstract   pdf
Real world players often increase their payoffs by voluntarily committing to play a fixed strategy, prior to the start of a strategic game. In fact, the players may further benefit from commitments that are conditional on the commitments of others.
This paper proposes a model of conditional commitments that unifies earlier models while avoiding circularities that often arise in such models. A commitment folk theorem shows that the potential of voluntary conditional commitments is essentially unlimited. All feasible and individuallyrational payoffs of a two-person strategic game can be attained at the equilibria of one (universal) commitment game that uses simple commitment devices. The commitments are voluntary in the sense that each player maintains the option of playing the game without commitment, as originally defined.
• Adam Tauman Kalai, Michael Mitzenmacher, and Madhu Sudan
  Tight Asymptotic Bounds for the Deletion Channel with Small Deletion Probabilities
  In Proc. IEEE International Symposium on Information Theory (ISIT), 2010.
  
abstract   pdf
In this paper, we consider the capacity C of the binary deletion channel for the limiting case where the deletion probability p goes to 0. It is known that for any p < 1/2, the capacity satisfies C >= 1?H(p), where H is the standard binary entropy. We show that this lower bound is essentially tight in the limit, by providing an upper bound C <= 1?(1?o(1))H(p), where the o(1) term is understood to be vanishing as p goes to 0. Our proof utilizes a natural counting argument that should prove helpful in analyzing related channels.
• Adam Tauman Kalai, Michal Feldman, and Moshe Tennenholtz
  Playing Games without Observing Payoffs
  In Innovations in Computer Science (ICS), 2010.
  
pdf
There is no abstract available for this paper.
• Aaron Roth, Nina Balcan , Adam Kalai, and Yishay Mansour
  On the Equilibria of Alternating Move Games
  Proceedings of the Twenty-first Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2010.
  
abstract   pdf
We consider computational aspects of alternating move games, repeated games in which players take actions at alternating time steps rather than playing simultaneously. We show that alternating move games are more tractable than simultaneous move games: we give an FPTAS for computing an ε-approximate equilibrium of an alternating move game with any number of players. In contrast, it is known that for k >= 3 players, there is no FPTAS for computing Nash equilibria of simultaneous move repeated games unless P = PPAD. We also consider equilibria in memoryless strategies, which are guaranteed to exist in two player games. We show that for the special case of k = 2 players, all but a negligible fraction of games admit an equilibrium in pure memoryless strategies that can be found in polynomial time. Moreover, we give a PTAS to compute an ε- approximate equilibrium in pure memoryless strategies in any 2 player game that admits an exact equilibrium in pure memoryless strategies.
• Christian Borgs, Jennifer Chayes, Adam Tauman Kalai, Azarakhsh Malekian, and Moshe Tennenholtz
  A novel approach to propagating distrust
  WINE 2010.
  abstract   pdf


Trust propagation is a fundamental topic of study in the theory and practice of ranking and recommendation systems on networks. The Page Rank algorithm ranks web pages by propagating trust throughout a network, and similar algorithms have been designed for recommendation systems. How might one analogously propagate distrust as well? This is a question of practical importance and mathematical intrigue. However, it has proven challenging to model distrust propagation in a manner which is both logically consistent and psychologically plausible. We propose a novel and simple extension of the Page Rank equations, and argue that it naturally captures most types of distrust that are expressed in such networks. We give an efficient algorithm for implementing the system and prove desirable properties of the system.

2009

• Adam Tauman Kalai, Alex Samorodnitsky, and Shang-Hua Teng
  Learning and Smoothed Analysis
  Proceedings of the 50th Annual Symposium on Computer Science (FOCS), 2009
  
abstract   pdf   pdf (long version)   slides (ppt)

We give a new model of learning motivated by smoothed analysis (Spielman and Teng, 2001). In this model, we analyze two new algorithms, for PAC-learning DNFs and agnostically learning decision trees, from random examples drawn from a constant-bounded product distributions. These two problems had previously been solved using membership queries (Jackson, 1995; Gopalan et al, 2005). Our analysis demonstrates that the "heavy" Fourier coefficients of a DNF suffice to recover the DNF. We also show that a structural property of the Fourier spectrum of any boolean function over "typical" product distributions. In a second model, we consider a simple new distribution over the boolean hypercube, one which is symmetric but is not the uniform distribution, from which we can learn O(log n)- depth decision trees in polynomial time.
• Adam Tauman Kalai and Varun Kanade
  Potential-based agnostic boosting
  NIPS 09
  
abstract   pdf
We prove strong noise-tolerance properties of a potential-based boosting algorithm, similar to MadaBoost (Domingo and Watanabe, 2000) and SmoothBoost (Servedio, 2003). Our analysis is in the agnostic framework of Kearns, Schapire and Sellie (1994), giving polynomial-time guarantees in presence of arbitrary noise. A remarkable feature of our algorithm is that it can be implemented without reweighting examples, by randomly relabeling them instead. Our boosting theorem gives, as easy corollaries, alternative derivations of two recent nontrivial results in computational learning theory: agnostically learning decision trees (Gopalan et al, 2008) and agnostically learning halfspaces (Kalai et al, 2005). Experiments suggest that the algorithm performs similarly to MadaBoost.
• Adam Tauman Kalai and Ravi Sastry
  The Isotron Algorithm: High-Dimensional Isotonic Regression
  Proceedings of the 22nd Annual Conference on Learning Theory (COLT), 2009.
  
abstract   pdf
The Perceptron algorithm elegantly solves binary classification problems that have a margin between positive and negative examples. Isotonic regression (fitting an arbitrary increasing function in one dimension) is also a natural problem with a simple solution. By combining the two, we get a new simple regression algorithm in high dimensions, with strong guarantees.
• Varun Kanade, Adam Kalai, and Yishay Mansour
  Reliable Agnostic Learning
  Proceedings of the 22nd Annual Conference on Learning Theory (COLT), 2009.
  abstract   pdf


We give efficient algorithms for learning in a model of learning with one-sided agnostic noise, such as a model of SPAM emails in which legit emails come from one set but SPAM emails may be distributed arbitrarily. The goal is to achieve an accuracy as high as possible while maintaining a near-zero rate of false positives. We show how to learn the class of DNFs using membership queries in this setting.

2008

• Parikshit Gopalan, Adam Tauman Kalai, and Adam R. Klivans
  Agnostically Learning Decision Trees
  In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC), pp. 527-536, 2008
  abstract   pdf   Slides (ppt)
We consider the problem of learning a decision tree in the presence of arbitrary noise. More formally, we are given black-box access (a type of active learning) to an arbitrary binary function on n bits, and our output is a function whose accuracy is almost as good as that of the best size-s decision tree, where accuracy is measured over the uniform distribution on inputs.
• Christian Borgs, Jennifer Chayes, Nicole Immorlica, Adam Tauman Kalai, Vahab Mirrokni, and Christos Papadimitriou
  The Myth of the Folk Theorem
  In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC), pp. 365-372, 2008
  
abstract   pdf
The folk theorem for repeated games suggests that repeated games should by easier to play than one-shot games. This can be made formal by giving an efficient algorithm for finding Nash equilibria in any repeated game with two players. Perhaps surprisingly, we show that for three or more players, it is as hard to find Nash equilibria in repeated games as it is in one-shot games.
• Adam Tauman Kalai, Yishay Mansour, and Elad Verbin
  Agnostic Boosting and Parity Learning
  To appear in Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC), pp. 629-638, 2008
  
abstract   pdf   slides (ppt)
We give the first boosting algorithm that is capable of handling arbitrary noise and boosting to optimal accuracy. We give an application to the problem of learning parity with arbitrary noise, over an arbitrary distribution.
• Reid Andersen, Christian Borgs, Jennifer Chayes, Uriel Feige, Abraham Flaxman, Adam Tauman Kalai, Vahab Mirrokni, Moshe Tennenholtz
  Trust-Based Recommendation Systems: an Axiomatic Approach
  To appear in Proceedings of the 17th international conference on World Wide Web (WWW), 2008
  
abstract   pdf
We cast the trust-based recommendation system problem as a voting problem on a graph with a partial +/- assignment, where each node receives a personalized recommendation. We consider natural axioms that lead to a unique algorithm, as well alternative axioms that lead to impossibility.

2007

• Adam Tauman Kalai
  Learning Nested Halfspaces and Uphill Decision Trees
  In Proceedings of 20th Annual Conference on Learning Theory (COLT), pp. 378-392, 2007
  
abstract   pdf
Predicting class probabilities and other real-valued quantities is often more useful than binary classification, but comparatively little work in PAC-style learning addresses this issue. We show that two rich classes of real-valued functions are learnable in the probabilistic-concept framework of Kearns and Schapire. The classes naturally generalize halfspaces, decision lists, and SVMs.
• Sham Kakade, Adam Tauman Kalai, and Katrina Ligett
  Playing Games with Approximation Algorithms
  In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC), pp. 546-555, 2007. Subsequently published in SIAM J. on Computing, 2009
  
abstract   pdf
How should one play a large repeated two-person game when you can only compute approximate best responses? How should one adaptively solve repeated optimization problems that are so complex that one can only approximately solve the offline (full-information) counterpart? This paper answers these two questions. The approach builds on a nice algorithm of Zinkevich (2003) and is very different from the previous work (for the exact cases) due to Hannan (1957) and Kalai and Vempala (2005, see below).
• Eli Ben-Sasson, Adam Tauman Kalai, and Ehud Kalai
  An Approach to Bounded Rationality
  In Advances in Neural Information Processing Systems 19 (NIPS), pp. 145-152, 2007
  
abstract   pdf
Many interactions in complex environments, e.g., chess, are affected by computational limitations. An extreme example is the factoring game, where the first player chooses a large number and sends it to the second player who then attempts to factor it. Ignoring computational considerations, the second player can factor any number and win, but with computational considerations the game seems to favor the first player. This well-known issue in game-theory falls under the term bounded rationality, yet there is no general model of playing games with computational limitations. (Prior work focused mainly on the case of finite automata playing repeated games like prisoner's dilemma.) We propose an extremely simple model of a game with additional costs (computational or otherwise) for each strategy. We illustrate that this model fits nicely into existing concepts in game theory such as zero-sum games, potential games, and submodular games, showing that natural learning dynamics continue to converge to equilibrium.

2006

• Ivona Bezakova, Adam Tauman Kalai, and Rahul Santhanam
  Graph Model Selection using Maximum Likelihood
  In Proceedings of the 23rd International Conference on Machine Learning (ICML), pp. 105-112, 2006
  
abstract   pdf
In recent years, a number of random graph models, such as preferential attachment, have been proposed as probabilistic models of large graphs. We suggest an objective method for ranking their performance on actual graphs. In particular, we look at the probability that a model assigns to a given graph, and design efficient MCMC algorithms for estimating these quantities.
• Elad Hazan, Adam Tauman Kalai, Satyen Kale, and Amit Agarwal
  Logarithmic Regret Algorithms for Online Convex Optimization
  In Proceedings of 19th Annual Conference on Learning Theory (COLT), pp. 499-513, 2006.
  
abstract   pdf
We present improved algorithms for the problem of online optimization, that use second derivatives, analogous to Newton's method.
• Adam Tauman Kalai and Santosh Vempala
  Simulated Annealing for Convex Optimization
  Math of OR, 31(2), pp. 253-266, 2006
  
abstract   pdf   slides: 15-min ppt   slides: 50-min ppt
Simulated annealing is a general-purpose optimization technique that has proven useful in practice, but is notoriously difficult to analyze. We show that it can be used for the problem of minimizing a linear function over a convex set, where the set is specified only by a membership oracle. Moreover, its guaranteed convergence rate is faster than that of any known alternative algorithm.

2005

• Abraham Flaxman , Adam Tauman Kalai, and Brendan McMahan
  Online Convex Optimization in the Bandit Setting: Gradient Descent Without a Gradient
  In Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 385-394, 2005
  
abstract   pdf   slides: 20-min ppt   slides: 50-min ppt
In many problems, a decision-maker has to make a sequence of decisions online, with limited feedback. For example, consider a company has to choose how much to spend in advertising through a number of channels each month. The feedback the company receives may be only the company's total profit that period. Such feedback is indirect and noisy -- it may be more influenced by the economy than the company's choices during that period. To model such problems, we consider a fixed convex feasible set. On the ith period, the decision maker chooses a feasible point x_i, and receives some reward, f_i(x_i), where f_i is any bounded concave function. The only feedback the decision maker receives is this reward f_i(x_i) -- no other information is revealed about f_i. We give an efficient algorithm that guarantees an average reward that approaches the best average reward achievable by a single feasible point, where the best is chosen with the benefit of hindsight. These guarantees hold for an arbitrary sequence of bounded concave functions.
• Sham Kakade and Adam Tauman Kalai.
  From Batch to Transductive Online Learning
  In Advances in Neural Information Processing Systems 18, 2006 (NIPS 05). (20-min NIPS ppt)
  
abstract   pdf
We consider the online transductive learning (Ben-David, Kushilevitz and Mansour, 1995) model where an arbitrary sequence of examples are presented to a learner, one at a time. The learner must predict each label, online, given only the labels of the previous examples and the future unlabeled examples. In contrast, more standard i.i.d. models of learning assume that examples are drawn independently and identically distributed from a fixed distribution. We give an algorithm that employs unlabeled data to convert any efficient learning algorithm in an i.i.d. setting to an efficient learning algorithm in the more difficult online transductive model.
• Adam Tauman Kalai, Adam Klivans, Yishay Mansour, and Rocco Servedio
  Agnostically Learning Halfspaces
  In Proceedings of the 46th Annual Symposium on the Foundations of Computer Science (FOCS), pp. 11-20, 2005
  
abstract   pdf  pdf (long version)   slides: 15-min FOCS ppt
The agnostic model of learning (Kearns, Schapire, and Sellie, 1992) is a natural model of learning where one aims to do as well as the best function in a given class of functions. Unfortunately, there are many previous negative and impossibility results for agnostic learning, due to computational intractability. We give a new algorithm for agnostic learning, based on the celebrated learning algorithm of Linial, Mansour, and Nisan. We show that, under mild distributional assumptions, it learns to predict as well as the best halfspace, in n dimensions. The algorithm does not suffer from the ``curse of dimensionality -- it runs in time polynomial rather than exponential in the dimension n.
• Sanjoy Dasgupta, Adam Tauman Kalai, and Claire Monteleoni
  Analysis of Perceptron-Based Active Learning
  In Proceedings of 18th Annual Conference on Learning Theory (COLT), 2005.
  
abstract   pdf
In active learning, the set of unlabeled examples is known in advance, and the learner can choose which examples are labeled as training data. We give a simple and efficient active learning procedure based on the classic Perceptron algorithm. Under distributional assumptions, the number of points that must be labeled to achieve any error rate is logarithmic in the desired error rate.
• Adam Tauman Kalai and Rocco Servedio
  Boosting in the Presence of Noise
  Journal of Computer and System Sciences 71(3): 266-290, 2005
  
abstract   pdf   pdf (STOC version)
Boosting is a technique that attempts to improve the accuracy of any learning algorithm. It has both strong theoretical guarantees as well as overwhelming empirical success. One often-cited weakness of boosting is its inability to deal with noisy data, even when the noise is chosen completely randomly and independently. Following work of Kearns, Mansour, and McAllester, we show that a simple divide-and-conquer boosting algorithm can boost optimally in the presence of noise.
• Adam Tauman Kalai and Santosh Vempala
  Efficient Algorithms for On-line Optimization
  Journal of Computer and System Sciences 71(3): 291-307, 2005
  
abstract   pdf   pdf (COLT version)
In online optimization, one wants to solve a sequence of combinatorial optimization problems in the face of uncertainty. For example, each day one wants to choose a path to drive to work, and only afterwards, one finds out the times on the various roads. Suppose that one can efficiently solve the one-shot version of the optimization problem, e.g., one can easily find the shortest path in a graph with known times. We give an efficient procedure for adaptively choosing solutions to a sequence of such problems, where the average quality of the solution approaches that of the best single solution. This holds for an arbitrary sequence of problems, yet guarantees are given with respect to the best solution, chosen with the benefit of hindsight. Our algorithm is as efficient as the best offline solution, i.e., the fastest algorithm to solve the problem if the entire sequence were known in advance.

2004

• Adam Tauman Kalai
  Learning Monotonic Linear Functions
  In Proceedings of 17th Annual Conference on Learning Theory, pp. 487-501
  
abstract   pdf   pdf (long version)   slides: 50min (ppt)
Generalized Additive Models (Hastie and Tibshirani) are a broad generalization of both linear and logistic regression. We give the first computationally efficient algorithm that provably learns this class of models. It is efficient in two sense: its runtime is polynomial in the size of the training data, and its error approaches optimal at a rate that is inverse polynomial.

2003

• Avrim Blum, Suchi Chawla, and Adam Tauman Kalai
  Static Optimality and Dynamic Search Optimality in Lists and Trees
  Algorithmica 36:3, pp. 249-260, 2003.
  
abstract   pdf   SODA version (ps file)
Splay Trees are an efficient algorithm for maintaining a dynamic binary search tree, popular both in theory and practice. They are guaranteed to be only a constant factor worse than the best possible static binary search tree. We give algorithms that are only (1+eps) worse than the best fixed binary search tree, and similar results for lists.
• Avrim Blum, Adam Tauman Kalai, and Hal Wasserman
  Noise-Tolerant Learning, the Parity Problem, and the Statistical Query Model
  JACM 50(4):506--519, 2003.
  
abstract   pdf   STOC version (pdf)
The parity with noise learning problem is one of the most beautiful problems in computer science that is believed to be hard. It is not only believed to be hard on worst-case instances but also on random instances. An efficient algorithm for this problem would find applications in many fields, such as error-correcting codes. We give the fastest-known algorithm. While it is not truly efficient, it is the first solution that is faster than brute force.
• Adam Tauman Kalai
  Generating Random Factored Numbers, Easily
  Journal of Cryptology 16(4):287-289, 2003.
  
abstract   pdf   SODA version (pdf)
Our goal is to generate a uniformly random number between 1 and N, along with its prime factorization. Since there are no known efficient factoring algorithms, one cannot simply generate a random number and then factor it. Eric Bach's award-winning dissertation introduces and solves this problem. We present a four-line solution that is still efficient. (See also this web page).

<2003

• Adam Tauman Kalai
  Efficient Pattern-Matching with Don't Cares
  In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 655-656, 2002.
  
abstract   ps file
We give a randomized algorithm for the string matching with don't cares problem, the standard string matching problem with wildcards. We present a four-line solution that is slightly faster and much simpler than previous algorithms.
• Adam Tauman Kalai
  Better computers for better people
  Ph.D. thesis, technical report CMU-CS-01-132, 2001
  
abstract   pdf
On the surface, the three on-line machine learning problems analyzed in this thesis may seem unrelated. The first is an on-line investment strategy introduced by Tom Cover. We begin with a simple analysis that extends to the case of fixed-percentage transaction costs. We then describe an efficient implementation that runs in time polynomial in the number of stocks. The second problem is k-fold cross validation, a popular technique in machine learning for estimating the error of a learned hypothesis. We show that this is a valid technique by comparing it to the hold-out estimate. Finally, we discuss work towards a dynamically-optimal adaptive binary search tree algorithm.
• Adam Tauman Kalai and Santosh Vempala
  Efficient Algorithms for Universal Portfolios
  Journal of Machine Learning Research 3(3):423--440, 2002
  
abstract   pdf   FOCS version (ps file)
The Universal Portfolio is an investment strategy introduced by Thomas Cover. Previously, all known implementations required computation exponential in the number of stocks. In this paper, we use random walks for an implementation that is polynomial in the number of stocks.
• Adam Tauman Kalai and Ehud Kalai
  Strategic Polarization
  Journal of Mathematical Psychology, 45:4, pp. 656-663, 2001.
  
abstract   ps file
An example of polarization is a marriage in which one spouse gives generously to charity while the other donates nothing. This may misrepresent what is, in actuality, a small discrepancy in preferences. It may be that the donating spouse would like to see 10% of their combined income go to charity each year, while the apparently frugal spouse would like to see 9% donated. A simple game-theoretic analysis suggests that the spouses will end up donating 10% and 0%, respectively. This paper gives a strategic (game-theoretic) analysis of polarization.
• Avrim Blum, Carl Burch, and Adam Tauman Kalai
  Finely Competitive Paging
  In Proceedings of the 40th Annual Symposium on the Foundations of Computer Science (FOCS), pp. 450-458, 1999
  
abstract   ps file
In the on-line paging problem, one has a fixed-size cache. Each time a page is requested that is not in the cache, it has to be brought in at a cost of 1 and another page has to be evicted from the cache. We present an algorithm that has the same worst-case performance as the previous algorithms, but for a large and important class of request sequences, is superior.
• Heung-Yeung Shum, Adam Tauman Kalai, and Steve Seitz
  Omnivergent Stereo
  Journal of Computer Vision 48:3, pp 159-172, 2002. (also at ICCV 1999)
  
abstract   pdf
We describe the design of an optimal camera for 3D reconstruction. In our model, a camera may capture a fixed number of pixels (light rays) from anywhere inside the circular frame of the camera. Afterwards, points outside the camera must be reconstructed as accurately as possible. We show that capturing tangent rays (in both directions) gives optimal uniform reconstructions.
• Avrim Blum, Adam Tauman Kalai, and John Langford
  Beating the Holdout: Bounds for K-Fold and Progressive Cross-Validation
  In Proceedings of the 10th Annual Conference on Computational Learning Theory (COLT), 1999
  
abstract   ps file
K-Fold cross-validation is a popular technique in machine learning for estimating the performance of a learned hypothesis on a data set. We provide the first theoretical justification for this method that shows that it is, on average, more accurate than a held-out test set of comparable size.
• Stan Chen, Adam Tauman Kalai, Avrim Blum, and Roni Rosenfeld
  On-line Algorithms for Combining Language Models
  In Proceedings of the International Conference on Accoustics, Speech, and Signal Processing, 1999.
  
abstract   ps file
We show how Cover's Universal Portfolios can be applied to the field of language modeling. The goal of a language model is to accurately predict the next word in a sequence of words, with applications to speech recognition and data compression. In this setting, the universal guarantees are very striking. We support this with experiments on several different corpora.
• Avrim Blum and Adam Tauman Kalai
  Universal Portfolios With and Without Transaction Costs
  Machine Learning 35:3, pp 193-205, 1999
  
abstract   ps file   15-min COLT slides (html)
We present a much simpler analysis of Thomas Cover's Universal Portfolios. This analysis easily extends to the case of transaction costs.
• Adam Tauman Kalai and Mel Siegel
  Improved Rendering of Parallax Panoramagrams for a Time-Multiplexed Autostereoscopic Display
  In Stereoscopic Displays and Applications IX: Proceedings of SPIE 3295, 1998
  
abstract   ps file
We describe a new kind of 3D display that is viewable without glasses.
• Avrim Blum and Adam Tauman Kalai
  A Note on Learning from Multiple-Instance Examples
  Machine Learning 30:1, pp. 23-30, 1998
  
abstract   ps file
In the multiple-instance learning setting introduced by Dietterich et al, the example data consist of n-tuples of points. An n-tuple is labeled positive if any of the n constituent points are positive. We show that this problem can be reduced to that of learning in the presence of noise.