21 research outputs found
'Arranged' Marriage, Co-Residence and Female Schooling: a Model with Evidence from India
We model the consequences of parental control over choice of wives for sons, for parental incentives to educate daughters, when the marriage market exhibits competitive dowry payments and altruistic but paternalistic parents benefit from having married sons live with them. By choosing uneducated brides, some parents can prevent costly household partition. Paternalistic self-interest consequently generates low levels of female schooling in the steady state equilibrium. State payments to parents for educating daughters fail toraise female schooling levels. Policies (such as housing subsidies) that promote nuclear families, interventions against early marriages, and state support to couples who marry against parental wishes, are however all likely to improve female schooling. We offer evidence from India consistent with our theoretical analysis.Arranged marriage, Dowry, Bride price, Female literacy, Marriage markets, Stable marriage allocation.
The Rate of Convergence of AdaBoost
The AdaBoost algorithm was designed to combine many "weak" hypotheses that
perform slightly better than random guessing into a "strong" hypothesis that
has very low error. We study the rate at which AdaBoost iteratively converges
to the minimum of the "exponential loss." Unlike previous work, our proofs do
not require a weak-learning assumption, nor do they require that minimizers of
the exponential loss are finite. Our first result shows that at iteration ,
the exponential loss of AdaBoost's computed parameter vector will be at most
more than that of any parameter vector of -norm bounded by
in a number of rounds that is at most a polynomial in and .
We also provide lower bounds showing that a polynomial dependence on these
parameters is necessary. Our second result is that within
iterations, AdaBoost achieves a value of the exponential loss that is at most
more than the best possible value, where depends on the dataset.
We show that this dependence of the rate on is optimal up to
constant factors, i.e., at least rounds are necessary to
achieve within of the optimal exponential loss.Comment: A preliminary version will appear in COLT 201
âArrangedâ Marriage, Co-Residence and Female Schooling: A Model with Evidence from India
We model the consequences of parental control over choice of wives for sons, for parental incentives to educate daughters, when the marriage market exhibits competitive dowry payments and altruistic but paternalistic parents benefit from having married sons live with them. By choosing uneducated brides, some parents can prevent costly household partition. Paternalistic self-interest consequently generates low levels of female schooling in the steady state equilibrium. State payments to parents for educating daughters fail to raise female schooling levels. Policies (such as housing subsidies) that promote nuclear families, interventions against early marriages, and state support to couples who marry against parental wishes, are however all likely to improve female schooling. We offer evidence from India consistent with our theoretical analysis.arranged marriage, dowry, bride price, female literacy, marriage markets, stable marriage allocation
The Rate of Convergence of AdaBoost
The AdaBoost algorithm was designed to combine many âweakâ hypotheses that perform slightly better than random guessing into a âstrongâ hypothesis that has very low error. We study the rate at which AdaBoost iteratively converges to the minimum of the âexponential lossâ. Unlike previous work, our proofs do not require a weak-learning assumption, nor do they require that minimizers of the exponential loss are finite. Our first result shows that the exponential loss of AdaBoost's computed parameter vector will be at most Δ more than that of any parameter vector of â[subscript 1]-norm bounded by B in a number of rounds that is at most a polynomial in B and 1/Δ. We also provide lower bounds showing that a polynomial dependence is necessary. Our second result is that within C/Δ iterations, AdaBoost achieves a value of the exponential loss that is at most Δ more than the best possible value, where C depends on the data set. We show that this dependence of the rate on Δ is optimal up to constant factors, that is, at least Ω(1/Δ) rounds are necessary to achieve within Δ of the optimal exponential loss.National Science Foundation (U.S.) (Grant IIS-1016029)National Science Foundation (U.S.) (Grant IIS-1053407
Game theory and optimization in boosting
Boosting is a central technique of machine learning, the branch of
artificial intelligence concerned with designing computer
programs that can build increasingly better models of reality as
they are presented with more data.
The theory of boosting is based on the observation that combining several models
with low predictive power can often lead to a significant boost in
the accuracy of the combined meta-model.
This approach, introduced about twenty years ago, has been a
prolific area of research, and has proved
immensely successful in practice.
However, despite extensive work, many basic questions about boosting
remain unanswered.
In this thesis, we increase our understanding of three such
theoretical aspects of boosting.
In Chapter 2 we study the convergence
properties of the most well known boosting algorithm, AdaBoost.
Rate bounds for this important algorithm are known for only special
situations that rarely hold in practice.
Our work guarantees fast rates hold under all situatons, and
the bounds we provide are optimal.
Apart from being important for practitioners, this bound also has
implications for the statistical properties of AdaBoost.
Like AdaBoost, most boosting algorithms are used for classification
tasks, where the object
is to create a model that can categorize relevant input data into
one of a finite number of different classes.
The most commonly studied setting is binary classification, when
there are only two possible classes, although the tasks arising in
practice are almost always multiclass in nature.
In Chapter 3 we provide a broad and general
framework for studying boosting for multiclass classification.
Using this approach, we are able
to identify for the first time the minimum assumptions under which
boosting the accuracy is possible in the multiclass setting.
Such theory existed previously for boosting for binary
classification, but straightforward extensions of that to the
multiclass setting lead to assumptions that are either too strong or
too weak for boosting to be effectively possible.
We also design boosting algorithms using these minimal assumptions,
which work in more general situations than previous
algorithms that assumed too much.
In the final chapter, we study the problem of learning from expert
advice which is closely related to boosting.
The goal is to extract useful advice from the opinions of a group of
experts even when there is no consensus among the experts
themselves.
Although algorithms for this task enjoying excellent guarantees have
existed in the past, these were only approximately optimal, and
exactly optimal strategies were known only when the experts gave
binary ``yes/no'' opinions.
Our work derives exactly optimal strategies when the experts provide
probabilistic opinions, which can be more nuanced than deterministic
ones.
In terms of boosting, this provides the optimal way of combining
individual models that attach confidence rating to their predictions
indicating predictive quality