Releasing Private Contingency Tables

Statistical agencies such as the US Census Bureau routinely release aggregate statistics about the general population. These statistics are often reported in the form of contingency tables. A 2-dimensional contingency table is an (m + 1) × (n + 1) matrix over two attributes that are binned into m rows and n columns. For instance, the attributes could be Age binned into buckets of length 10 and Height binned into buckets of length 5. For each cell (i, j) in the matrix, the table reports an aggregate value called the cell value. This is often an aggregate of some private attribute of the population. For example, the table may report the total number of individuals with diabetes in each cell of the table. In this case, the private attribute being aggregated is Boolean, either 1 if the individual has diabetes or 0 if he does not. The final row i = m + 1 (resp., column j = n + 1) contains the total row (resp., column) sums, e.g., the total number of individuals in each row who have diabetes. Besides the cell values, the total number of individuals that fall in each cell is also publicly known, e.g., the total number of individuals in the age range 10-20 years and height range 165-170 cm, regardless of whether or not they have diabetes.