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Amir Globerson

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Published work

29 published item(s)

preprint2026arXiv

Controllable User Simulation

Using offline datasets to evaluate conversational agents often fails to cover rare scenarios or to support testing new policies. This has motivated the use of controllable user simulators for targeted, counterfactual evaluation, typically implemented by prompting or fine-tuning large language models. In this work, we formalize controllable simulation as a causal inference problem. By bridging natural language evaluation with off-policy evaluation methodology, we show that the standard practice of training simulators via supervised fine-tuning on post-hoc trajectory labels yields a structurally biased model. Specifically, these labels are inextricably coupled to the data-generating behavior policy, injecting a look-ahead bias that breaks causal consistency. Furthermore, we prove that under policy shift this failure causes the variance of evaluation metrics to explode geometrically, a phenomenon we term controllability collapse. To restore causal consistency, we establish theoretical conditions for accurate simulation and propose practical training mitigations: a priori controls, step-wise dynamic controls, and direct policy-conditioned learning. Empirical evaluation confirms that while standard global controls distort conversational distributions and collapse behavioral diversity, our causally grounded simulators eliminate look-ahead bias, preserve natural variance, and exhibit robust zero-shot generalization to unseen agent behaviors.

preprint2026arXiv

Cost-Aware Learning

We consider the problem of Cost-Aware Learning, where sampling different component functions of a finite-sum objective incurs different costs. The objective is to reach a target error while minimizing the total cost. First, we propose the Cost-Aware Stochastic Gradient Descent algorithm for convex functions, and derive its cost complexity to attain an error of $ε$. Furthermore, we establish a lower bound for this setting and provide a subset selection algorithm to further reduce the cost of training. We apply our theoretical insights to reinforcement learning with language models, where the computational cost of policy gradients varies with sequence length. To this end, we introduce Cost-Aware GRPO, an algorithm designed to reduce the cost of policy optimization while preserving performance. Empirical results on 1.5B and 8B LLMs demonstrate that our approach reduces the tokens used in policy optimization by up to about 30% while matching or exceeding baseline accuracy.

preprint2022arXiv

Active Learning with Label Comparisons

Supervised learning typically relies on manual annotation of the true labels. When there are many potential classes, searching for the best one can be prohibitive for a human annotator. On the other hand, comparing two candidate labels is often much easier. We focus on this type of pairwise supervision and ask how it can be used effectively in learning, and in particular in active learning. We obtain several insightful results in this context. In principle, finding the best of $k$ labels can be done with $k-1$ active queries. We show that there is a natural class where this approach is sub-optimal, and that there is a more comparison-efficient active learning scheme. A key element in our analysis is the "label neighborhood graph" of the true distribution, which has an edge between two classes if they share a decision boundary. We also show that in the PAC setting, pairwise comparisons cannot provide improved sample complexity in the worst case. We complement our theoretical results with experiments, clearly demonstrating the effect of the neighborhood graph on sample complexity.

preprint2022arXiv

Learning to Retrieve Passages without Supervision

Dense retrievers for open-domain question answering (ODQA) have been shown to achieve impressive performance by training on large datasets of question-passage pairs. In this work we ask whether this dependence on labeled data can be reduced via unsupervised pretraining that is geared towards ODQA. We show this is in fact possible, via a novel pretraining scheme designed for retrieval. Our "recurring span retrieval" approach uses recurring spans across passages in a document to create pseudo examples for contrastive learning. Our pretraining scheme directly controls for term overlap across pseudo queries and relevant passages, thus allowing to model both lexical and semantic relations between them. The resulting model, named Spider, performs surprisingly well without any labeled training examples on a wide range of ODQA datasets. Specifically, it significantly outperforms all other pretrained baselines in a zero-shot setting, and is competitive with BM25, a strong sparse baseline. Moreover, a hybrid retriever over Spider and BM25 improves over both, and is often competitive with DPR models, which are trained on tens of thousands of examples. Last, notable gains are observed when using Spider as an initialization for supervised training.

preprint2022arXiv

Object-Region Video Transformers

Recently, video transformers have shown great success in video understanding, exceeding CNN performance; yet existing video transformer models do not explicitly model objects, although objects can be essential for recognizing actions. In this work, we present Object-Region Video Transformers (ORViT), an \emph{object-centric} approach that extends video transformer layers with a block that directly incorporates object representations. The key idea is to fuse object-centric representations starting from early layers and propagate them into the transformer-layers, thus affecting the spatio-temporal representations throughout the network. Our ORViT block consists of two object-level streams: appearance and dynamics. In the appearance stream, an "Object-Region Attention" module applies self-attention over the patches and \emph{object regions}. In this way, visual object regions interact with uniform patch tokens and enrich them with contextualized object information. We further model object dynamics via a separate "Object-Dynamics Module", which captures trajectory interactions, and show how to integrate the two streams. We evaluate our model on four tasks and five datasets: compositional and few-shot action recognition on SomethingElse, spatio-temporal action detection on AVA, and standard action recognition on Something-Something V2, Diving48 and Epic-Kitchen100. We show strong performance improvement across all tasks and datasets considered, demonstrating the value of a model that incorporates object representations into a transformer architecture. For code and pretrained models, visit the project page at \url{https://roeiherz.github.io/ORViT/}

preprint2022arXiv

On the Implicit Bias of Gradient Descent for Temporal Extrapolation

When using recurrent neural networks (RNNs) it is common practice to apply trained models to sequences longer than those seen in training. This "extrapolating" usage deviates from the traditional statistical learning setup where guarantees are provided under the assumption that train and test distributions are identical. Here we set out to understand when RNNs can extrapolate, focusing on a simple case where the data generating distribution is memoryless. We first show that even with infinite training data, there exist RNN models that interpolate perfectly (i.e., they fit the training data) yet extrapolate poorly to longer sequences. We then show that if gradient descent is used for training, learning will converge to perfect extrapolation under certain assumptions on initialization. Our results complement recent studies on the implicit bias of gradient descent, showing that it plays a key role in extrapolation when learning temporal prediction models.

preprint2022arXiv

Structured Video Tokens @ Ego4D PNR Temporal Localization Challenge 2022

This technical report describes the SViT approach for the Ego4D Point of No Return (PNR) Temporal Localization Challenge. We propose a learning framework StructureViT (SViT for short), which demonstrates how utilizing the structure of a small number of images only available during training can improve a video model. SViT relies on two key insights. First, as both images and videos contain structured information, we enrich a transformer model with a set of \emph{object tokens} that can be used across images and videos. Second, the scene representations of individual frames in video should "align" with those of still images. This is achieved via a "Frame-Clip Consistency" loss, which ensures the flow of structured information between images and videos. SViT obtains strong performance on the challenge test set with 0.656 absolute temporal localization error.

preprint2022arXiv

Visual Prompting via Image Inpainting

How does one adapt a pre-trained visual model to novel downstream tasks without task-specific finetuning or any model modification? Inspired by prompting in NLP, this paper investigates visual prompting: given input-output image example(s) of a new task at test time and a new input image, the goal is to automatically produce the output image, consistent with the given examples. We show that posing this problem as simple image inpainting - literally just filling in a hole in a concatenated visual prompt image - turns out to be surprisingly effective, provided that the inpainting algorithm has been trained on the right data. We train masked auto-encoders on a new dataset that we curated - 88k unlabeled figures from academic papers sources on Arxiv. We apply visual prompting to these pretrained models and demonstrate results on various downstream image-to-image tasks, including foreground segmentation, single object detection, colorization, edge detection, etc.

preprint2021arXiv

An Optimization and Generalization Analysis for Max-Pooling Networks

Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However, these architectures are not well understood from a theoretical perspective. For example, we do not understand when they can be globally optimized, and what is the effect of over-parameterization on generalization. Here we perform a theoretical analysis of a convolutional max-pooling architecture, proving that it can be globally optimized, and can generalize well even for highly over-parameterized models. Our analysis focuses on a data generating distribution inspired by pattern detection problem, where a "discriminative" pattern needs to be detected among "spurious" patterns. We empirically validate that CNNs significantly outperform fully connected networks in our setting, as predicted by our theoretical results.

preprint2021arXiv

On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent

Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime solution, whereas small initialization leads to so called "rich regimes". However, the initialization structure is richer than the overall scale alone and involves relative magnitudes of different weights and layers in the network. Here we show that these relative scales, which we refer to as initialization shape, play an important role in determining the learned model. We develop a novel technique for deriving the inductive bias of gradient-flow and use it to obtain closed-form implicit regularizers for multiple cases of interest.

preprint2020arXiv

Differentiable Scene Graphs

Reasoning about complex visual scenes involves perception of entities and their relations. Scene graphs provide a natural representation for reasoning tasks, by assigning labels to both entities (nodes) and relations (edges). Unfortunately, reasoning systems based on SGs are typically trained in a two-step procedure: First, training a model to predict SGs from images; Then, a separate model is created to reason based on predicted SGs. In many domains, it is preferable to train systems jointly in an end-to-end manner, but SGs are not commonly used as intermediate components in visual reasoning systems because being discrete and sparse, scene-graph representations are non-differentiable and difficult to optimize. Here we propose Differentiable Scene Graphs (DSGs), an image representation that is amenable to differentiable end-to-end optimization, and requires supervision only from the downstream tasks. DSGs provide a dense representation for all regions and pairs of regions, and do not spend modelling capacity on areas of the images that do not contain objects or relations of interest. We evaluate our model on the challenging task of identifying referring relationships (RR) in three benchmark datasets, Visual Genome, VRD and CLEVR. We describe a multi-task objective, and train in an end-to-end manner supervised by the downstream RR task. Using DSGs as an intermediate representation leads to new state-of-the-art performance.

preprint2020arXiv

Holdout SGD: Byzantine Tolerant Federated Learning

This work presents a new distributed Byzantine tolerant federated learning algorithm, HoldOut SGD, for Stochastic Gradient Descent (SGD) optimization. HoldOut SGD uses the well known machine learning technique of holdout estimation, in a distributed fashion, in order to select parameter updates that are likely to lead to models with low loss values. This makes it more effective at discarding Byzantine workers inputs than existing methods that eliminate outliers in the parameter-space of the learned model. HoldOut SGD first randomly selects a set of workers that use their private data in order to propose gradient updates. Next, a voting committee of workers is randomly selected, and each voter uses its private data as holdout data, in order to select the best proposals via a voting scheme. We propose two possible mechanisms for the coordination of workers in the distributed computation of HoldOut SGD. The first uses a truthful central server and corresponds to the typical setting of current federated learning. The second is fully distributed and requires no central server, paving the way to fully decentralized federated learning. The fully distributed version implements HoldOut SGD via ideas from the blockchain domain, and specifically the Algorand committee selection and consensus processes. We provide formal guarantees for the HoldOut SGD process in terms of its convergence to the optimal model, and its level of resilience to the fraction of Byzantine workers. Empirical evaluation shows that HoldOut SGD is Byzantine-resilient and efficiently converges to an effectual model for deep-learning tasks, as long as the total number of participating workers is large and the fraction of Byzantine workers is less than half (<1/3 for the fully distributed variant).

preprint2020arXiv

Learning Canonical Representations for Scene Graph to Image Generation

Generating realistic images of complex visual scenes becomes challenging when one wishes to control the structure of the generated images. Previous approaches showed that scenes with few entities can be controlled using scene graphs, but this approach struggles as the complexity of the graph (the number of objects and edges) increases. In this work, we show that one limitation of current methods is their inability to capture semantic equivalence in graphs. We present a novel model that addresses these issues by learning canonical graph representations from the data, resulting in improved image generation for complex visual scenes. Our model demonstrates improved empirical performance on large scene graphs, robustness to noise in the input scene graph, and generalization on semantically equivalent graphs. Finally, we show improved performance of the model on three different benchmarks: Visual Genome, COCO, and CLEVR.

preprint2020arXiv

Learning Object Permanence from Video

Object Permanence allows people to reason about the location of non-visible objects, by understanding that they continue to exist even when not perceived directly. Object Permanence is critical for building a model of the world, since objects in natural visual scenes dynamically occlude and contain each-other. Intensive studies in developmental psychology suggest that object permanence is a challenging task that is learned through extensive experience. Here we introduce the setup of learning Object Permanence from data. We explain why this learning problem should be dissected into four components, where objects are (1) visible, (2) occluded, (3) contained by another object and (4) carried by a containing object. The fourth subtask, where a target object is carried by a containing object, is particularly challenging because it requires a system to reason about a moving location of an invisible object. We then present a unified deep architecture that learns to predict object location under these four scenarios. We evaluate the architecture and system on a new dataset based on CATER, and find that it outperforms previous localization methods and various baselines.

preprint2016arXiv

Learning to generalize to new compositions in image understanding

Recurrent neural networks have recently been used for learning to describe images using natural language. However, it has been observed that these models generalize poorly to scenes that were not observed during training, possibly depending too strongly on the statistics of the text in the training data. Here we propose to describe images using short structured representations, aiming to capture the crux of a description. These structured representations allow us to tease-out and evaluate separately two types of generalization: standard generalization to new images with similar scenes, and generalization to new combinations of known entities. We compare two learning approaches on the MS-COCO dataset: a state-of-the-art recurrent network based on an LSTM (Show, Attend and Tell), and a simple structured prediction model on top of a deep network. We find that the structured model generalizes to new compositions substantially better than the LSTM, ~7 times the accuracy of predicting structured representations. By providing a concrete method to quantify generalization for unseen combinations, we argue that structured representations and compositional splits are a useful benchmark for image captioning, and advocate compositional models that capture linguistic and visual structure.

preprint2016arXiv

Optimal Tagging with Markov Chain Optimization

Many information systems use tags and keywords to describe and annotate content. These allow for efficient organization and categorization of items, as well as facilitate relevant search queries. As such, the selected set of tags for an item can have a considerable effect on the volume of traffic that eventually reaches an item. In settings where tags are chosen by an item's creator, who in turn is interested in maximizing traffic, a principled approach for choosing tags can prove valuable. In this paper we introduce the problem of optimal tagging, where the task is to choose a subset of tags for a new item such that the probability of a browsing user reaching that item is maximized. We formulate the problem by modeling traffic using a Markov chain, and asking how transitions in this chain should be modified to maximize traffic into a certain state of interest. The resulting optimization problem involves maximizing a certain function over subsets, under a cardinality constraint. We show that the optimization problem is NP-hard, but nonetheless has a simple (1-1/e)-approximation via a simple greedy algorithm. Furthermore, the structure of the problem allows for an efficient implementation of the greedy step.To demonstrate the effectiveness of our method, we perform experiments on three tagging datasets, and show that the greedy algorithm outperforms other baselines.

preprint2014arXiv

Tight Error Bounds for Structured Prediction

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each depending on two specific labels. Intuitively, the more pairwise terms are used, the better the expected accuracy. However, there is currently no theoretical account of this intuition. This paper takes a significant step in this direction. We formulate the problem as classifying the vertices of a known graph $G=(V,E)$, where the vertices and edges of the graph are labelled and correlate semi-randomly with the ground truth. We show that the prospects for achieving low expected Hamming error depend on the structure of the graph $G$ in interesting ways. For example, if $G$ is a very poor expander, like a path, then large expected Hamming error is inevitable. Our main positive result shows that, for a wide class of graphs including 2D grid graphs common in machine vision applications, there is a polynomial-time algorithm with small and information-theoretically near-optimal expected error. Our results provide a first step toward a theoretical justification for the empirical success of the efficient approximate inference algorithms that are used for structured prediction in models where exact inference is intractable.

preprint2013arXiv

Learning Max-Margin Tree Predictors

Structured prediction is a powerful framework for coping with joint prediction of interacting outputs. A central difficulty in using this framework is that often the correct label dependence structure is unknown. At the same time, we would like to avoid an overly complex structure that will lead to intractable prediction. In this work we address the challenge of learning tree structured predictive models that achieve high accuracy while at the same time facilitate efficient (linear time) inference. We start by proving that this task is in general NP-hard, and then suggest an approximate alternative. Briefly, our CRANK approach relies on a novel Circuit-RANK regularizer that penalizes non-tree structures and that can be optimized using a CCCP procedure. We demonstrate the effectiveness of our approach on several domains and show that, despite the relative simplicity of the structure, prediction accuracy is competitive with a fully connected model that is computationally costly at prediction time.

preprint2013arXiv

Tighter Linear Program Relaxations for High Order Graphical Models

Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP) relaxation with unary consistency constraints between the HOP and the individual variables. In many cases, the resulting relaxations are loose, and in these cases the results of inference can be poor. It is thus desirable to look for more accurate ways of performing inference in these models. In this work, we study the LP relaxations that result from enforcing additional consistency constraints between the HOP and the rest of the model. We address theoretical questions about the strength of the resulting relaxations compared to the relaxations that arise in standard approaches, and we develop practical and efficient message passing algorithms for optimizing the LPs. Empirically, we show that the LPs with additional consistency constraints lead to more accurate inference on some challenging problems that include a combination of low order and high order terms.

preprint2012arXiv

Convergent message passing algorithms - a unifying view

Message-passing algorithms have emerged as powerful techniques for approximate inference in graphical models. When these algorithms converge, they can be shown to find local (or sometimes even global) optima of variational formulations to the inference problem. But many of the most popular algorithms are not guaranteed to converge. This has lead to recent interest in convergent message-passing algorithms. In this paper, we present a unified view of convergent message-passing algorithms. We present a simple derivation of an abstract algorithm, tree-consistency bound optimization (TCBO) that is provably convergent in both its sum and max product forms. We then show that many of the existing convergent algorithms are instances of our TCBO algorithm, and obtain novel convergent algorithms "for free" by exchanging maximizations and summations in existing algorithms. In particular, we show that Wainwright's non-convergent sum-product algorithm for tree based variational bounds, is actually convergent with the right update order for the case where trees are monotonic chains.

preprint2012arXiv

Convergent Propagation Algorithms via Oriented Trees

Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these optimization problems. However, there are few convergence guarantees for such algorithms, and the algorithms are therefore not guaranteed to solve the corresponding optimization problem. Here we present an oriented tree decomposition algorithm that is guaranteed to converge to the global optimum of the Tree-Reweighted (TRW) variational problem. Our algorithm performs local updates in the convex dual of the TRW problem - an unconstrained generalized geometric program. Primal updates, also local, correspond to oriented reparametrization operations that leave the distribution intact.

preprint2012arXiv

Convexifying the Bethe Free Energy

The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.

preprint2012arXiv

Discriminative Learning via Semidefinite Probabilistic Models

Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art results. One shortcoming of these models is that their output (known as the 'margin') is not calibrated, and cannot be translated naturally into a distribution over the labels. Thus, it is difficult to incorporate such models as components of larger systems, unlike probabilistic based approaches. The second type of approach constructs class conditional distributions using a nonlinearity (e.g. log-linear models), but is occasionally worse in terms of classification error. We propose a supervised learning method which combines the best of both approaches. Specifically, our method provides a distribution over the labels, which is a linear function of the model parameters. As a consequence, differences between probabilities are linear functions, a property which most probabilistic models (e.g. log-linear) do not have. Our model assumes that classes correspond to linear subspaces (rather than to half spaces). Using a relaxed projection operator, we construct a measure which evaluates the degree to which a given vector 'belongs' to a subspace, resulting in a distribution over labels. Interestingly, this view is closely related to similar concepts in quantum detection theory. The resulting models can be trained either to maximize the margin or to optimize average likelihood measures. The corresponding optimization problems are semidefinite programs which can be solved efficiently. We illustrate the performance of our algorithm on real world datasets, and show that it outperforms 2nd order kernel methods.

preprint2012arXiv

Learning the Experts for Online Sequence Prediction

Online sequence prediction is the problem of predicting the next element of a sequence given previous elements. This problem has been extensively studied in the context of individual sequence prediction, where no prior assumptions are made on the origin of the sequence. Individual sequence prediction algorithms work quite well for long sequences, where the algorithm has enough time to learn the temporal structure of the sequence. However, they might give poor predictions for short sequences. A possible remedy is to rely on the general model of prediction with expert advice, where the learner has access to a set of $r$ experts, each of which makes its own predictions on the sequence. It is well known that it is possible to predict almost as well as the best expert if the sequence length is order of $\log(r)$. But, without firm prior knowledge on the problem, it is not clear how to choose a small set of {\em good} experts. In this paper we describe and analyze a new algorithm that learns a good set of experts using a training set of previously observed sequences. We demonstrate the merits of our approach by applying it on the task of click prediction on the web.

preprint2012arXiv

Sufficient Dimensionality Reduction with Irrelevant Statistics

The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two variables, one often seeks a compact representation of one variable which preserves information about the other variable. We have recently introduced ``Sufficient Dimensionality Reduction' [GT-2003], a method that extracts continuous reduced dimensional features whose measurements (i.e., expectation values) capture maximal mutual information among the variables. However, such measurements often capture information that is irrelevant for a given task. Widely known examples are illumination conditions, which are irrelevant as features for face recognition, writing style which is irrelevant as a feature for content classification, and intonation which is irrelevant as a feature for speech recognition. Such irrelevance cannot be deduced apriori, since it depends on the details of the task, and is thus inherently ill defined in the purely unsupervised case. Separating relevant from irrelevant features can be achieved using additional side data that contains such irrelevant structures. This approach was taken in [CT-2002], extending the information bottleneck method, which uses clustering to compress the data. Here we use this side-information framework to identify features whose measurements are maximally informative for the original data set, but carry as little information as possible on a side data set. In statistical terms this can be understood as extracting statistics which are maximally sufficient for the original dataset, while simultaneously maximally ancillary for the side dataset. We formulate this tradeoff as a constrained optimization problem and characterize its solutions. We then derive a gradient descent algorithm for this problem, which is based on the Generalized Iterative Scaling method for finding maximum entropy distributions. The method is demonstrated on synthetic data, as well as on real face recognition datasets, and is shown to outperform standard methods such as oriented PCA.

preprint2012arXiv

The Minimum Information Principle for Discriminative Learning

Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we argue that for classiffication tasks, mutual information is a more suitable information theoretic measure to be optimized. We show how the principle of minimum mutual information generalizes that of maximum entropy, and provides a comprehensive framework for building discriminative classiffiers. A game theoretic interpretation of our approach is then given, and several generalization bounds provided. We present iterative algorithms for solving the minimum information problem and its convex dual, and demonstrate their performance on various classiffication tasks. The results show that minimum information classiffiers outperform the corresponding maximum entropy models.

preprint2012arXiv

Tightening LP Relaxations for MAP using Message Passing

Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation and, when the relaxation is tight, provably find the MAP configuration. The standard LP relaxation is not tight enough in many real-world problems, however, and this has lead to the use of higher order cluster-based LP relaxations. The computational cost increases exponentially with the size of the clusters and limits the number and type of clusters we can use. We propose to solve the cluster selection problem monotonically in the dual LP, iteratively selecting clusters with guaranteed improvement, and quickly re-solving with the added clusters by reusing the existing solution. Our dual message-passing algorithm finds the MAP configuration in protein sidechain placement, protein design, and stereo problems, in cases where the standard LP relaxation fails.

preprint2012arXiv

What Cannot be Learned with Bethe Approximations

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By failure we mean that the empirical marginals cannot be recovered from the approximated maximum likelihood parameters (i.e., moment matching is not achieved). We provide several conditions on empirical marginals that yield outer and inner bounds on the set of Bethe learnable marginals. An interesting implication of our results is that there exists a large class of marginals that cannot be obtained as stable fixed points of belief propagation. Taken together our results provide a novel approach to analyzing learning with Bethe approximations and highlight when it can be expected to work or fail.

preprint2011arXiv

Gaussian Robust Classification

Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In order to acheive this goal, it is important to carefully design the learner, so it will not overfit the training data. The later can is done usually by adding a regularization term. The statistical learning theory explains the success of this method by claiming that it restricts the complexity of the learned model. This explanation, however, is rather abstract and does not have a geometric intuition. The generalization error of a classifier may be thought of as correlated with its robustness to perturbations of the data: a classifier that copes with disturbance is expected to generalize well. Indeed, Xu et al. [2009] have shown that the SVM formulation is equivalent to a robust optimization (RO) formulation, in which an adversary displaces the training and testing points within a ball of pre-determined radius. In this work we explore a different kind of robustness, namely changing each data point with a Gaussian cloud centered at the sample. Loss is evaluated as the expectation of an underlying loss function on the cloud. This setup fits the fact that in many applications, the data is sampled along with noise. We develop an RO framework, in which the adversary chooses the covariance of the noise. In our algorithm named GURU, the tuning parameter is a spectral bound on the noise, thus it can be estimated using physical or applicative considerations. Our experiments show that this framework performs as well as SVM and even slightly better in some cases. Generalizations for Mercer kernels and for the multiclass case are presented as well. We also show that our framework may be further generalized, using the technique of convex perspective functions.